Velocity factor is something that applies inside the coax, where the fields are all inside the dielectric medium. Antennas in the air are not subject to "velocity factor".
A plastic coating on an antenna does load it a bit, and reduce its length, but this is mostly relevant at much higher frequencies. For example in printed circuit antennas at 2.4 GHz, where the PCB is a relevant fraction of a wavelength, the shortening effect can be 10 or 15%. Also if you get a build-up of ice on UHF yagi antennas, maybe even VHF, they can be detuned enough to stop working. At 160 metres, a realistic thickness of plastic will make no significant difference to the resonant frequency.
The dipole on the website is described badly. It may work, by using the coax to do two things - 1) as the antenna itself and 2) as a short-circuit stub which provides an inductive load at the open end, near the feedpoint. Now coax is not a good antenna material, it's heavy, high wind resistance, not very strong and will be damaged by water if it gets the slightest cut in the jacket. And inductors are best made with coils of wire, but a stub will work and may have advantages on other bands. You might choose to coil it up so the weight is at the centre, and extend the antenna with strong thin wire. Finally it has no balun. So I don't recommend this design.
To suggest some things for 160 m in a limited space:
Loading, in the form of inductors, will shorten any antenna. It doesn't make a short antenna more efficient, but that's just the deal at 160 m. You could reduce the antenna size to about half of full size before this becomes impractical.
Monopole-type antennas are half the size of dipoles, so consider a "long wire" or "inverted L" or similar, fed against a ground stake or mesh. Full length would be 40 metres of wire but with an inductor at the feed, 20-30 metres would be enough. Depending on your ground, you will also need some further matching, either your ATU or a parallel capacitor and some tuning of the inductor.
Height above ground is not a hard rule. At 160 it's impractical to be half a wavelength high anyway, so work with what you have.
If you make a dipole, you should include a balun, otherwise the coax will radiate (which doesn't matter) and you will have RF in your shack, affecting your computers and other things. A monopole doesn't have a balun but depends on a good ground.