Do they have fighting games there

They have games from the 80z through 2000z. Vs-Fighting, MPRPGs, old classics, 90z classics, shooting games, a couple of table tops and a few pinball machines.

They have a little bit of everything and rotate them out pretty frequently.. there's always something new when I go there..

Is it just old school games or are there recent fighting games there too

Omg...yes

I saw at least Mortal Kombat II and Street Fighter (don't remember which).

Yes. Many.