There are tons of options here for connecting to another PC, so knowing exactly what you want, will require a little more knowledge about what you want to do:
Assumption: You're using Windows XP, Vista, 7, 8/8.1 on both PCs
1) Do you want to open Files?
With Windows this is very easy to setup. You can create a HomeGroup or add files to a Public folder so anyone on your LAN network can see them:
See this Microsoft link here.
2) Are you trying to control the gaming PC remotely?
Again, with Windows this is possible. Push START -> Run... and type "msra.exe" or you can start typing "msra" on Windows 7 and newer and it searches for you. MSRA is a Remote Assistance app that guides you through how you can establish a connection between two computers.
This article should help you do this.
3) Do you want to do Game/Movie streaming?
This will be trickier, if you don't use option #2. But its possible with 3rd party software, (most likely not free). I know that NVIDIA and Steam both are developing/or have developed, streaming software, but I'm not sure about those, since I haven't used them. If you're interested in
NVIDIA's solution its here, and
Steam's solution is here.
Hope this helps!