Almost any modern NVidia card will do 4K video editing, it all depends how fast you want to get the job done. Personally, I wouldn't look at anything lower than a GTX 1060 6GB, but not knowing your budget, I don't know if you're looking for something better or something cheaper.
BTW, what resolution are you going to be using for the gaming? If 1080p, then the GTX 1060 6GB will be fine. If it's 4K, you're going to need a better GPU for that, like a 1080 or 1080ti, these of course will be faster at video editing work too.