I do not play any flash games. I prefer my windows games, plays better. Not sure why the linux games are cheesy at best. Perhaps it is the language they is being used. Remember this is opensource. Opensource programs are not that powerful like, for say, C+ or c#.
Most linux based games are programmed in C++, as for C# that is now a .net language in which you can program it through the mono library. Those are all possible. The big distinction is that the major software companies which make those "pretty" graphics are not interested in the Linux users side of the market, in many cases the only time they think about support Linux based systems is to run as the game server rather than the client.