The best way I have found to size a chain--and the method described in Shimano's Dealer Manuals for their rear derailleurs--is the wrap method. You take the chain while it isn't woven thru the derailleur and place it on the large chainring and largest cassette cog. Orient the chain so that it is tight and that it comes together at the backside of the large cassette cog. There will be an excess of chain links past where the ends of the chain come together. You then add 2 or three links* from where the chain comes together on the back of the cassette to determine where the chain should be broke. If you're using a quick link to rejoin the chain, you'll need both ends of the chain to be inner links (the quick link is a set of outer link plates, it also counts as one link past the where the chain wrap comes together).
Here's some screenshots of rear derailleur install instructions from Shimano for clarity. Note, the first photo's information of adding 2-3 links pertains to your situation. The second photo is from Shimano 12 speed rear derailleur instructions and is included here to better show the chain wrap method. You do NOT need to add the number of links shown here in your system. You'll use 2 or 3, with a quick link counting as one and the other plus 1 or 2 depending on what you need for a termination (inner or outer).


Based on your photo's, I think you're fine, but obviously based on the numbers provided in your comment, your new chain has quite a few more links than the old chain. The wrap method works best because it incorporates the length of the chain stays in its measurement. Given any bike with seven to 11 speed systems, the chain wrap +2-3 links method yields a correctly sized chain.
*By "links" here I really mean half links: an inner link=1 the outer link plates =1 use of a quick link counts as 1, though it usually is not yet on the chain being wrapped. Technically, one chain link is one inner PLUS one outer link, however this is not what we count in the above method, which counts ½ links as one whole number.