Hi there!
I'm usually making my templates based on models pulled from games. Most older games you just need a converter that can convert the format the game uses to something usable by editor. (as mentioned in previous posts)
For newer ones you usually need an extractor that can get the models (still in the game format) from the container files, then convert them to something useful. (e.g. Unreal Engine 3 uses .upk files which you have to get the .psk models from which you can convert to something useful, oh and on some occasions upk files are in another container file for reasons like its part of a dlc or whatnot)
There are also programs that can make "model screenshots" of the screen that is on your monitor at the moments, as in dumping the mesh and the textures on your HDD from the VRAM. I think most games have some sort of protection against it, and the newer DirectX versions are also either unsupported or protected against this (I can be wrong though I generally don't use this method.)
Also yeah game models are usually messy as hell internally with a lot of clipping that you have to clean up if you want to unfold. I guess it depends on your skills which one is faster: building a model or cleaning up a game one. I for one know enough about 3D modelling to clean up the models internally fairly decently, even to lower the poly count to a build-able level, but I couldn't build a decent 3D model if my life depended on it from scratch.
As for the site you liked in, I don't actually know how hard would it be to get that particular model, never tried to pull one from a website before. From my admittedly limited knowledge of browser based 3D rendering I think it would be fairly well embedded in the site so accessing it wouldn't be trivial.