I've only done it with OBS MP, not sure that the original version can send over UDP.
You can use UDP under the recording tab, the settings I've used are below. For the URL, that needs to be the IP of the computer you're sending to on your network plus an arbitrary port number (1234 will do). Note: I've got my bitrate at 50,000. I have a gigabit network so this causes no issues for me but you may need to adjust this. I suspect there's no real benefit to it being this high but I haven't really experimented all that much.
On the recording PC, add a Media Source and put the Input as udp://0.0.0.0:1234 (or whatever port number you used) and then click OK. Hit Record on your gaming PC and you should see whatever you're sending on the recording PC (I seem to remember having to restart OBS on the recorder before it would work).
Excelent program. I've been searching for a similar application for 6 months and just now I found it. I use OBS in my church and my hard task is to send the annoucement video that is projected to the congregation to another PC used to transmit the worship. I tried Wirecast and it has the remote desktop that do this job (and works very well). When I started to use OBS, I couldn't do that, even using rtmp and nginx ou nonaserver. FFMpeg send packets as expected, but the delay intermittently occurs. It's not reliable, at least in my case, and I guess the alternative showed by Fantus_Longhorn will have the same issue. Besides that, it is a tough task to open OBS in the transmitter machine when you can simply execute a tiny program.
I hope OBS developers can create a remote desktop similar program and make it as part of OBS app.