Yea, get an FX-8350 and throw on some weak-as graphics card like a GT210 for a display output.
Its easier to give an editing rig gaming capabilities than it is a gaming rig good editing. So make an editing rig now, then throw on a decent card later when you can afford it.
The 6300 will probably do worse than an i5 and forever trail it in gaming. The i5 will do better at video editing than the 6300, and a gaming beast down the road if you ever add a high-end graphics card to the mix.
If you can get an 8350, it will be a stronger video editing rig than either the 6300 or the i5. (And it's not bad at gaming when you add a good GPU)
I chose these two builds due to price and Microcenter $40 bucks off mobo deals which I will drive down to this weekend. 8350 would've been an option but given the fact that it requires a GPU which ups the cost over the 3570k, I've eliminated it out of the running. Thanks. My budget is definitely under 750 with all pieces.
If he's into gaming then the FX-6300+650 ti is the best option, no way you're going to play games with a 210 GT or intel hd 4000, and for video editing a nvidia card with a good quantity of cuda cores is important.
You can pick a i5-3470 in microcenter for 150$, if you could pay the same for the 650 ti, you have the two things.