What kind of logical fallacy in this argument?

You ask what sort of fallacy captures the spirit of the argument:

"In the past, there was no country called Japan. Sushi was created when Japan was not yet called Japan as it is today. Therefore, Sushi is not a Japanese dish."

According to some, it is the definist or definitional fallacy.

The definist fallacy consists of (1) defining one concept in terms of another concept with which it is not clearly synonymous, (2) as the persuasive definition fallacy, defining a concept in terms of another concept in an infelicitous way that is favorable to one's position, or (3) the insistence that a term be defined before it can be used in discussion. (emphasis mine)

That is to say, the argument rests on an obvious hidden premise: that to be a Japanese dish requires it to have been invented during the time of the modern nation state of Japan. This of course is absurd. How much of Japanese culture, food or otherwise, was invented before the modern nation state? This is a typical tactic of fallacious reasoning to get to desirable premises that are otherwise questionable or absurd, because it allows one to define words infelicitiously, to covertly reason from conclusion to premise, rather than the other way around, by changing definitions (SEP) in ways that tend to offend reason and convention. It's a tactic popular with those who promulgate conspiracy theories and crackpots.

Of hidden premises, it might be said that enthymemes are rather normal in argumentation, and the inclusion of the per se is not fallacious; rather it is the contents of that hidden premis that must be inspected when reasoning informally. What makes it a fallacy in this case is that we have logical objections stemming from the underlying semantics of the logic. Thus, having hidden premises does not necessarily make an argument fallacious; having a hidden premise where we assert an absurdity like only food invented after the establishment of the modern state is the rub. To call this premise out leaves the assertion only defensible by bickering over what it means to be Japanese, in which case one can merely respond with charges of equivocation.

EDIT: It is utterly bizarre that people that anyone would argue mochi and sushi are not Japanese foods. From both articles:

A mochi (/moʊtʃiː/ MOH-chee;1 Japanese もち, 餅 [motɕi] ⓘ) is a Japanese rice cake made...

Sushi (すし, 寿司, 鮨, 鮓, pronounced [sɯɕiꜜ] or [sɯꜜɕi] ⓘ) is a traditional Japanese dish made with vinegared rice...

Some people who have grievances against social reality believe that they can twist definitions and engaging in word games to try to deconstruct obvious empirical facts derived from the conventions of language; it is a sign of an irrational interlocutor. The following comments illustrate a good-natured attempt at trying to undermine an obvious empirical fact about how sushi and mochi are Japanese (and are included since moderators have taken to deleting comments where so inclined):

I agree on the definition being the key "catch" of the proposed fact, but this doesn't ring true as a logical fallacy. Not unless you can conclusively prove what the correct definition of calling something "Japanese" is (thereby invalidating all other interpretations), which is not as straightforward as you'd initially suspect. To offer a counterpoint to your claim that this is a fallacy: was the Colosseum built by Italians? Same location, right? I would agree that it's part of Italian cultural heritage, but I wouldn't say Italians built it. Whether it's then "an Italian building" is arguable. – Flater

@Flater it's not a formal fallacy, but it is an informal fallacy, which is also a kind of logical fallacy. – barbecue

@barbecue: Informal fallacies are still defined by being flawed, which implies there is a right answer (or definition, in this case) that should have been used, but wasn't. I disagree with your suggestion that this interpretation is provably wrong. Chiefly because I can both see cases where this distinction is justifiable and where it isn't (cfr my Roman/Italian example). Additionally, regardless of my feelings on the right definition, the quoted text elaborates on its definition. That is a transparent disclaimer that counters any suggestion that this is argued surreptitiously. – Flater

@Flater It certainly does meet the criteria of an informal according to Damer, but I'll leave that to the author to explain. As for both your call for proof and your counter example, both are easily dealt with. My daughter's Japanese tutor 小川先生 (Ogawa-sensei) assures me that both mochi and sushi are Japanese foods. I'd be an idiot to argue with a native of Japan (or the textbooks she has provided that it isn't a Japanese food). Of course, let's say you didn't have access to a Japanese teacher to ask... – J D

Well, then the source of truth would be the multiple dictionaries and encyclopedias that assure us that both foods are Japanese. To wit: "A mochi (/moʊtʃiː/ MOH-chee;1 Japanese もち, 餅 [motɕi] ⓘ) is a Japanese rice cake" and "Sushi (すし, 寿司, 鮨, 鮓, pronounced [sɯɕiꜜ] or [sɯꜜɕi] ⓘ) is a traditional Japanese dish made with vinegared rice". Since this seems mysterious to some of the contributors on this site that one cannot simply will a description of extremely wide-spread convention out of existence because it is conceivable that the definition might be otherwise (a bizarre form of egotism...) – J D

the basis for proof is that the term in question 'Japanese' applied to foods is the empirical facticity of the state of affairs of the convention of language. What makes the argument flawed (and strangely persuasive to amateur philosophers apparently) is that it arrives at the conclusion that the Japanese people (日本人, nihonjin) who are the experts on their own cuisine are somehow wrong, and a bunch of non-Japanese speakers who almost certainly have never been to Japan and have no Japanese language skills presume to declare the whole of the Japanese people mistaken about their own language and their own culture... – J D

Of course, you wouldn't be such a halfwit as to try to overrule hundreds of years of Japanese language convention of referring to もち or すし as Japanese foods, would you? If you did, you certainly would have been convinced by some sort of flawed argument. As @barbecue has pointed out, informal fallacies are grounded in the flawed semantics of a term. – J D

@Flater As for your Colosseum example, the difference between Roman architects (architecti Romani and architetti romani) is one of historical culture and language. The men who built the Colosseum spoke Latin and used techniques familiar to the Romans. Modern Romans speak Italian and use power tools. No one would confuse the two, and to argue that it is arguable what "Italian means" therefore the Colosseum is an Italian edifice would either be equivocation on the term 'Italian' or be a silly appeal to a continuum fallacy. - JD

It is not an act of language prescriptivism to use the conventions of a language; it is a necessary concession for communication to function properly. One may disagree with the convention of language, but one may not in good intellectual faith attempt to redefine the terms to alter the social construction of reality. At best, it's a disingenuous act, and at worst it is some form of propaganda.

The fallacy (and only in the broadest sense — perhaps better characterized as disingenuousness or simple lack of clarity) is assuming the unstated premise:

something can be a "Japanese" dish only if the thing was created after Japan was known as Japan.

Of course, it is open for people in a discussion to accept that as a premise, but in the argument in the question, it is missing or unstated.

The issue is not a fallacy but a premise that may be disputed.

The premise is this: that "the definition of a Japanese dish is a dish created in the country of Japan, as I have described it".

You may dispute this by saying: "no, the definition of a Japanese dish is a dish created by the ethnic people that now reside in the present-day country of Japan".

At this point you're discussing the underlying disagreement, which is the definition of a "Japanese dish".

A fallacy is a flaw in someone's reasoning so that the conclusion does not follow from the premises.

Now a huge problem with this argument is that it makes use of implicit definitions of words that are used very ambiguously. As a consequence it's very hard to argue whether this is or isn't a fallacy.

So you could for example read it as:

P1: A dish is a national dish if and only if it originates from a particular country
P2: Sushi and Mochi did not originate from (modern) Japan
C: Therefor they are not national dishes of (modern) Japan

Now if an argument like this follows the form that if P1 were true and P2 were true then C MUST also be true then it is valid and thus not a (formal) fallacy. If P1 and P2 further actually would be true (and hence also the conclusion), then it would be sound.

So while these might be unconventional definitions, for example pasta apparently didn't originate in Italy, yet few people would question Italy's tradition of pasta; you might nonetheless make such an argument which could be valid on it's own terms.

The problem however is that "originates from a particular country" is a very ambiguous term. And that's already more concrete than what was in the actual argument. So does country refer to the geographical place? Does it refer to the modern state? Does it refer to the nation? Does it refer to the ethnicity? So what if something is invented by a group of people before that group officially names itself as group? Did it then originate from that group, given that they are the same people or does the official naming matters? Or what about a tourist inventing something within a country, does that count? And so on.

So if you were to give a concrete answer to these questions it could be that the definition is odd sounding, but leads to a valid argument.

However without strict definition this can be read as a Motte-and-bailey fallacy where you make a more general claim and when challenged move it back to a more narrow claim that could be easier defended or it's cousin of the No True Scotsman, where you argue that it's not actually a "real/true national dish if it's just popular and has a long tradition but doesn't originate somewhere", so in other words you also adapt the definition halfway through. Though one should be careful people charging others with that may also be doing exactly that.

Or the other way around if the definition is fixed you might mess with the particular and introduce an equivocation for example using country for both geographic spot, nation, ethnicity, state, society, etc. Which might have overlaps, but which might have different implications with regards to the definition.

So TL;DR first and foremost it's not a complete argument so it depends on unstated specifics as to whether that is or isn't a fallacy.