I'm currently running a system with a i3 4130T and a GTX 1050 (non Ti) and it does fine with most of the gaming I do. For power I use a 160W HD-Plex DC board with a Dell Alienware 150W power brick. So the limit is with the power brick, and looks like it doesn't come close to its max wattage.
As others have said, four threads is enough overhead for gaming. The downside to my i3 is that it can't turbo boost for 1 or 2 threads. Kaby Lake Pentiums would though.
Also, you might actually notice a performance drop more in older games that don't take advantage of multithreading, like Source games such as Portal or TF2.