The only way I could see this working is if you were to hook up an Apple TV via an HDMI port on your PC monitor. From there, you could use AirPlay. There are some games specifically made with AirPlay in mind. They turn your iPhone into the controller. Select the link for how to play iPhone games on Apple TV in our ultimate guide to the Apple TV.
The same goes for Macs. There is no way to play iOS games on a Mac.