So your computer has two displays, and you want run a game in full screen mode on one monitor and simultaneously open browser on the other.
The key requirement here is full screen as when running in window mode, you can switch out of the game anytime you want like with any other program. When in full screen, the game limits mouse cursor and keyboard to itself. Of course you can press alt-tab to switch out of full screen game. But normally this collapses the game to a taskbar tab. Some games do not especially in windows 8 dual monitor stretch mode,but most do. A few solutions exist to address the issue so you can play on one display and surf on the other. The first one sells in Steam by the name of Actual Multiple Monitors. It does exactly what we want – keeps a game always in full screen mode on one of the monitors. The utility comes with a comprehensive description of what you need to do to enable the feature. Another similar app is DisplayFusion. It has many functions, one of which is to prevent active full screen game from closing when focus is switched away. So you can switch mouse and keyboard to a browser on another display without closing the full screen game. Another solution that might have the feature is UltraMon. It fixes a dozen issues with multi monitor setups, so go check it out. Another place worth checking out is your video card settings – most videocards come with Ati, Nvidia or Intel control center. Look for the option there. As for various wireless display technologies like WiDi, Miracast, Chromecast, Airplay – they are tailored mostly for media streaming and I doubt they can handle a full screen game. Besides they do require WiFi connection directly to the display, so if your PC gets internet connection over WiFi, it will have to go offline and use the adapter to connect to the display.