I recently got my RPi 3, even though I had planned to use it to control an autonomous robot, being a gamer at heart, I'm really very curious about whether or not it can run games, and if it can (like it runs the the Minecraft Pi edition) how will be the performance? Can regular Linux games be run on the RPi 3? Moreover, I don't have much knowledge about Windows 10 IoT, but can it run the usual windows games?
Win 10 IoT core differs quite much from "desktop" windows. It's highly likely that typical windows games will not run as is. Lets call that a reduced feature set.
Linux applications can be run if their binaries are provided for the ARMv7 architecture or if you can obtain the source and compile it yourself on the Pi or cross-compile it for the Pi. Obviously the computational power of the Pi is less than that of a typical desktop PC which could diminish the fun for power hungry games (if that is an issue).
I appreciate that you're a gamer. You must know that the number of possibilities are already jolly high! As a programmer, I have to say any game you choose to program for the RPi will run on it! As such the options are infinite.
I understand the Pi 3 graphics output on HDMI is superior to its predecessors, but what sort of game did you have in mind? 3D first-person shooters are probably a bit of a stretch.
Win 10 IoT don't provide desktop interface. If even it do you was aren't able to play games because most of games for x86 architecture and RPi based on ARM one.
Nevertheless, there are two great options to play games on RPi:
Quake III is easy to install on the Pi and it looks awesome. This shows what that little processor can do, though, my challenge is to get Quake II running. I'm making an Amiga in mine, but I expect that with so many units sold, new games (like Q3) will be developed to buy and install in the Pi. Obviously older games with 320 x 200 screens in 16 colors don't translate well to modern hardware but by the mid 90's RTG boards and 32 bit processing made high resolutions and huge color palettes programmable and I still get a kick out of Metal Slug and Cruisin' USA on the Pi. (It's hard to believe that was 25 years ago!)