Depends on the game you want to run and how much performance its engine needs. Some games would probably run fine on a Pi; some games would need a more powerful system. Some arcade systems supported by MAME have more processing power and specialized hardware than the Pi itself, even before taking into account the overhead of emulation.

But beyond that, a commercial MAME cabinet would require ROMs. People have built unofficial cabinets of questionable legality incorporating a pile of ROMs, but a commercial cabinet would require actually licensing specific games.

The Pi doesn't have the power to run some games.

I ran into problems with NeoGeo games.