I think that sort of game might be too slow.
=P This is actually helping narrow down requirements though, thanks.
So, ideally something that hardware performance would really hamper in-game performance (winning). I'm not sure if an RTS is great because while micro could be hampered, it might not make enough of a difference if the blob is still good (and nobody knows how to play).
An FPS where you stutter or have a low frame rate might hurt your aim, a MOBA might be good but I don't know about performance requirements yet...