I'm going to assume it's tower-only if you're trying to fit in a CPU like that under a 1K budget. I would highly recommend going to an i7 4770k and a good motherboard compared to using the 2011 socket. It'll be PLENTY for gaming, and will do your video editing perfectly.
If your spending 1000 dollars then you will have to skimp out on other components. Get the i5 4670k. Excellent for gaming. The i7 is for a workstation. You don't need the best thing in the world if your just gaming. It's better to just get a better gpu. Don't spend more on your cpu than your gpu. The i5 is perfect for what you need to do with it. The i7 is overkill. Only if you were doing intense hd video editing would you need an i7.
When it comes to 1080p gaming you need a good gpu. The cpu will help with frame times, and doesn't carry a whole lot of influence when it comes to 1080p gaming. If you were going to run a multi monitor setup and you were running it at 1440p then, yes, you would probably need the i7. For light video editing and next gen gaming all you need is an i5 4670k. And, yes you can overclock with a decent cpu cooler. I would recommend the coolermaster hyper 212 evo. You should have no problem getting it to 4ghz.
For a gpu go with the new r9 280x. The sapphire version of the card is great with performance. It comes in at about $299.99 for the regular version, and 330 dollars for the Overclocked version. If you plan on overclocking the card anyway, then just get the regular clocked version.
I would also encourage you to take R9 280x with 3570k, 3770k, 4670k or 4770k. System memory can be even 1333Mhz because you would be using intel and doing gaming which doesn't need system memory performance so much. So first priority is GPU then comes CPU after that you will check PSU and Mobo for them. I think the minimum PSU for these would be 550W. Bigger is fine for future upgrades.