I think Flashm could probably pin it down exactly as it is a Euro Corolla but it looks like a corolla
Here is a link to the original web page
http://www.gunstig.no/v2/?page=videoprod
Only some of the vids there actually work.
It really doesn't matter much an AE-86 is an AE-86 ... especially once you strip out the interior, replace the springs and swaybars with aftermarket equipment, install a full roll cage, and mod the engine, and either weld the diff or install a LSD.
Models and years just don't matter, you have an ae-86 shell, a 4 cylinder engine with 120-200 hp at the wheels depending on mods and low tight suspension.