We are entering an odd time of transition with games right now as the new consoles are both 8 core parts, which may mean that games in the near future may finally be able to take advantage of something bigger than a quad core, so take the following advice with a grain of salt and know that it applies mostly to today's games, and not games coming out in the near future:
1) If just for gaming then do not get an i7 processor. Games today only take advantage of 4 cores, and what few will take advantage of more cores only use real cores, not HT cores.
2) Generally speaking, games are far more GPU bound than CPU bound. A quad core i5 Intel or octo core FX AMD chip is going to be the way to go at the moment. As consoles are now all on AMD octo-core designs then there is a chance (but clearly no guarantee) that an AMD system may have an advantage going forward with new games that are designed primarily for new consoles. As a general rule of thumb you should get an adequate CPU and then pour the bulk of your money towards the GPU.
3) If you are really looking at your computer as a workhorse for gaming and video capture/edit/exporting then I would highly suggest stretching your budget to get a 6 core LGA2011 i7. The added 2 cores will give games a little boost, but having 12 threads of editing horsepower at your disposal will go a long way to keep capturing smooth and exporting painless. Even last gen's 2011 equipment is going to give significant content creation advantages even if it will not affect gaming performance much.
4) You need either a robust HDD array or an SSD (or both). When I converted up to an i7 for my video editing rig I had a hard time pushing the CPU past the 60% load mark when editing because my HDDs were simply not fast enough to keep the CPU busy. Even when running seperate drives for different types of content and scratch discs it was still not enough throughput to properly utilize the rest of the system. Upgrading to larger modern HDDs in a RAID array and having a system drive with SSD space for a scratch disc put the bottleneck back on the CPU where it belongs.