Okay I have no idea about fighting games, but here's some that have enlivened many an overly-long train trip:
I very highly recommend Rebuild....very entertaining "build a fort against zombie hordes" strategy game, in particular it's brutally fun at the higher difficulty levels. Not super polished but really good.
Great Big War Game is a fun turn-based-strategy-lite sort of thing
The Kairosoft "<something> story" games are pretty cool lite management sims. I'd recommend Grand Prix Story as their best, Epic Astro Story and Beastie Bay were also good
If you can get past the cutesy-ness, Where's My Water has a pretty clever puzzle game underneath
Pirates & Traders is pretty much a turn-based rip-off of Pirates! but I do not say that as a bad thing in any way, and also it's free