I7 3770 and i7 3770k is the jump worth it?

To answer yor question there will be no performane difference. The only reason to get a 3770K over the 3770 is if you plan on overclocking.

For gaming there is no point in getting the I7. You are paying 100 extra dollars for hyperthreading and extra cache two things games don't make use of. It has also been shown that the I7's hyperthreading can cause a 2% performance penalty. The I5 is more than enough for any game today.