For most games you will be fine, but any game that can use 4 or more cores may struggle. Like BF3/BF4 online multiplayer for example. If you can stretch it, I would suggest an i5 over the i3. You would get a lot more longevitiy out of it when it comes to gaming. Most games today are optimised to use at least 4 cores.
PS: The i3 is a dual core cpu with 2 threads to each core to simulate 4 cores. An i5 is 4 full power cores, and the i7 is 4 cores with 2 threads to each core. That would simulate being an 8 core CPU.