The answer is simple. The CPU is being overwhelmed because it only has 2 cores. Most games use two cores, and depending on the codec used video encoding may use 1 or 2 cores. So... your CPU is being maxed out by playing games and encoding video at the same time. The most obvious solution is to build a new PC with a quad core CPU. Of course, if you play a game that uses all 4 cores (not very many games), then encoding video at the same time will also decrease performance.
Encoding the video to a different physical hard drive than where the game is installed in can help improve performance a little bit, but only when the game needs to access the hard drive to load data, like maps.