I was asking this same question about a 4690K.. Sure games will continue to run fine on that CPU.
As far as how well they will run? I think that depends on the game and if the developers program support for multi-threading, in which case a 6-8+ threaded CPU *may* run the game better than the quad-core, non-hyper-threaded 6600K.
But overall, the 6600K should still be good for gaming for the next 4-5 years. Unless some major breakthrough in IPC or multi-threading becomes mainstream before then and games pick up the trend, *which is very possible.