TeamViewer and similar remote assistance programs aren't the best option for this because you connect to the other computer through their servers (mainly to avoid firewall and NAT issues), so your gaming session is send from your gaming computer to internet and then send back to your other computer.
In order to minimize lag and use the full bandwidth of your local network you need to use a remote program that use direct connections, like the integrated Remote Desktop (only for professional* versions of Windows) or some VNC variant like TightVNC.
Note that even with direct connections you may not get an acceptable performance since that tools are not designed for video or gaming.
* Although the Remote Desktop client is included in all versions of Windows the server is only available in professional/business/server editions, although there are some dubious hacks to workaround this (dubious in the legal sense, the hack itself seems safe).
1Any solution is going to introduce latency. What else have you tried other then Teamviewer? – Ramhound – 2017-09-28T19:08:29.603
I doubt if any remote desktop application will give adequate performance for gaming use. You might just achieve sufficient performance using dedicated hardware for remote monitor, keyboard and mouse, as this link suggests, but no guarantees.
– AFH – 2017-09-28T19:19:25.8631
You do want your computers in one LAN for sure and a solution that passes data entirely within LAN. With Steam games use Steam In-Home Streaming.
– Kamil Maciorowski – 2017-09-28T19:37:09.660ok so theres no technology yet for this problem – Raymond M – 2017-09-28T20:01:10.240