While I'm not a big fan of photography and cameras, I'd still go for the camera in your situation. It'll last longer, and you don't have to run the latest games on the highest settings. Lower the shadow quality from Ultra to Very High/High/Medium, and maybe the Texture Quality from Ultra/Very High to High or even Medium. Lower AA from x16/x12/x8 to maybe x4 or x2, or turn it off completely. Whenever I play a new game, I always turn down AA to the lowest option possible, without turning it off completely because I neither care or see a huge difference between the different AA options.
Also, look up guides for increasing performance in the games you want to play. A friend of mine has a computer almost identical to my computer, but he has a Radeon HD6950, so he usually end up tweaking .ini-files and a lot of other stuff to increase performance by even just a few frames per second.
The highest settings in a game doesn't automatically mean the best gaming experience.
When it comes to cameras and taking pictures of your family during holidays/vacations, or taking pictures of your dog or cat... Good quality pictures does make a difference. That dog or cat of yours won't live forever, same with your mom and dad, and memories can be forgotten. 20 years from now you might've forgotten all about that evening when you or your family did something really fun and crazy. Going back to look at the pictures 20 years later can bring back a lot of really good memories. Who knows, some of the pictures you might want to frame and hang on the wall. If the camera used is really bad at taking pictures without the flash, or in a dark room, the picture might not be as good.
I'm sorry for kinda rambling a bit here, and I'm really tired so some of this might not even make sense, but I'd really go for the camera in your situation. I'm guessing the camera will be shared with your family, while you're the only one who'll have use for the GTX 780? Anyway, this is just my opinion. In the end, you have the final say in what you spend your own money on.