Can it run them? Yes. Will it run them well? Eh...that will depend on the game.
Overwatch seems to be more than fine, able to reach 120FPS (http://www.techspot.com/review/1180-overwatch-benchmarks/page2.html). DOOM isn't too bad, as you can at least reach 60FPS (http://www.techspot.com/review/1173-doom-benchmarks/page2.html); same with Star Wars Battlefront (http://www.techspot.com/review/1096-star-wars-battlefront-benchmarks/). Rise of the Tomb Raider, however, shows issues; it barely reached 47FPS on the "High" quality, vs. the "Very High" quality setting (http://www.techspot.com/review/1128-rise-of-the-tomb-raider-benchmarks/page2.html). Witcher 3 is even worse, as it barely hit 40FPS (http://www.techspot.com/review/1006-the-witcher-3-benchmarks/page3.html).
It might be time to find a better card. For example, the RX 470 in Rise of the Tomb Raider had better performance on the "Very High" quality setting (http://www.techspot.com/review/1220-amd-radeon-rx-470/page4.html), with the RX 480 & GTX 1060 providing even more performance. It's not surprising, though, as the GTX 780 is now a couple of generations back, & considered the "equal" of the GTX 970 (http://www.tomshardware.com/reviews/gpu-hierarchy,4388.html), which is right where the GTX 1060 & RX 480 are falling.