An RDP client should do the job, I guess that Splashtop is pretty much that (remote access software) but there's a strong software licensing issue.
Perhaps it's working above on Windows 7 Professional or Ultimate and not working on Windows 8.1 "Home"?
Windows "Pro" at best barely lets you have two concurrent users (local + remote) which is useful for troubleshooting/user assistance purpose. Else, the official mantra is you need Windows Server 2008 or 2012 and a special remote desktop license per client.
If that theory is right, that Windows 7 which accepts one client wouldn't work with two clients.
Still, some software could ignore or bypass the Windows licensing (simply install some Windows or Linux in virtualbox or VMWare.. host Windows won't know/do something/care about it.)
Client/server programs are another : for example performance monitoring software that would include a web interface (i.e. a web server). Access it from a web browser on the tablet.
Likewise, web based or not (or both) there's some other software where a back-end can run on the PC and a front-end on the tablet : torrents, music players.
Miracast or whatever it's named could be great if you can have a "dummy" secondary monitor whose output is beamed through the network. (at worst, you would plug some stupid resistors in a VGA or DVI connector to make the PC think there's another display)
But compared to a "real" remote session or client/server software, I fear that any interaction with the software displayed on tablet will steal focus from your full screen game (not a biggie but still
). But mainly this wastes wifi spectrum. In the near future maybe Miracast / Wifi Direct would be sorted out
and you'd plug one USB Type C cable into the tablet which gives you power, USB2, USB3, and good wired ethernet at the same time.