In a gaming, (un)surprisingly, the only thing that really matters is the GPU.
The processor isn't as important and very few games benefit from better processors (off the top of my head, Skyrim, but not by a dramatic amount). Aside from that, many games made in the last 6 years were developed with ease of porting to consoles in mind, which for all intents and purposes lowered the requirement bar to ridiculous levels. I've read accounts that people were able to play Battlefield 3 just fine on a Celeron G1610 with a midrange video card.
Memory isn't all that important either. Most games are 32-bit and in Windows the memory usage limit for 32-bit programs is 2GB
, unless compiled with a flag to use all 4GB (again, Skyrim is the only game I know that was compiled this way). So 4GB is enough to scoot you by. Though if you are a heavy multitasker, you should probably consider 6GB or 8GB. More memory is only useful if you constantly run out and the system is thrashing away at the hard drive because it's accessing the swap file constantly. It doesn't improve performance ever
unless that scenario is happening
I also have no reason to believe that games in the near future will require
quad core processors. If developers are still developing with the ease of console porting in mind, then there's nothing really to worry about. That i3 will smoke the CPU in either the PS4 or Xbox One (by virtue that they're both using Netbook-class processors).
So really, the only upgrade you will need in the near future is a video card. And that's probably all that you will be upgrading until the system is so old that finding parts to upgrade it rather than outright building a new computer will be hard.