In general this is true however there are a few CPU intensive games where the processor makes a large difference as well, such as the Sims 2. Or if you are playing intense chess programs they can max out the CPU and take 5-10mins to move on a 2Ghz Athlon 64.
"I had pit two different chess programs against each other it ended in a stalemate, I would have lost in three moves since I suck at chess."