Um, nope, that isn't anywhere near enough for all of those things.
You might spend that much on a video capture card and HDCP decryptor. Video editing requires quite a bit of computational horsepower to have it done in a reasonable time as well as a lot of storage space to capture the raw video.
Low-end gaming can be achieved with $600 along with everyday use.
Normally I would suggest an i3 build for gaming but in your case I suggest an FX 6300.. You will really benefit from having more cores than few when it comes to rendering. And the 6300 isnt that much worse for games anyways.
Here is what I put together without an OS.. I assume you have it or will be buying separately:
A little less than $600
The GTX 750 ti has shadow play allowing you to record gameplay on the PC. The FX 8320 has 8 cores which is what you want for video editing
A little less than $600
The GTX 750 ti has shadow play allowing you to record gameplay on the PC. The FX 8320 has 8 cores which is what you want for video editing
This build has a much weaker GPU but a better CPU.. The PSU and HDD aren't as reliable though. So basically if you will render a lot get this build, if you will game more get my build!