Sad but true but the lowliest Sandy or better yet Ivy will blow any Penryn away.
Here is a bench comparing E8600 and i3-2100:
http://www.anandtech.com/bench/Product/54?vs=289
The i3-2100 is marginally faster in 5 out of 7 games, much much faster in one game, and marginally slower in 2 out of 7 games.
....But if the OP bought something like a e8400 it could be overclocked to a level beyond the stock e8600 speed. (Whereas Sandy/Ivy bridge dual cores cannot be overclocked.)
Unfortunately the OP also needs memory (adding to the total cost of the upgrade).
I guess it really depends on the specific game he wants to play... (eg, BF3 64 multiplayer is very popular and benchmarks I have seen indicate it does better with a quad core, but apparently is still playable with a fast dual core.)
......and his budget (a Sandy/Ivy Bridge i3 will require a new mobo, RAM kit and Windows License....plus his time (labor) to install.)
.