If it had to be done on a single pc, either a 6 or 8 core cpu. Even then with a hexcore cpu the video editing is likely to suffer some. It won't encode video while gaming at the same speed it would if you weren't gaming. James Mason had a good suggestion if it's possible. It's not impossible to encode while gaming, just expect there to be some tradeoffs.
It would also help to set up a single pc properly, aka an os/programs drive, game drive, video encoding drive with enough ram to support both tasks simultaneously. If you try and export converted video to the same drive your game is running on there's a chance of the data becoming bottlenecked and affecting one task or the other or both.
If you were to build dual systems the price could change some depending on the parts. For instance 16gb of ram aren't needed for a gaming rig. Going with an i7 6700 you could edit video using the stock cooler and save money there. Other various tweaks to preference.