Is there any software that allows this? I want to be able to play a game on my notebook when I'm away from home, while my gaming pc is on at home. Obviously I know this would introduce latency issues, but I'm thinking strategy games rather than FPS, so it shouldn't be an issue. Is it possible?

remote dekstop protocol or any RPD client.

examples are ...

windows rdp
teamviewer
logmein

these are used commonly by professionals such as peer review from American Economic Association prior to publishing and a ton of proctor testing websites.
Personally Logmein is more user friendly than the others, but maybe I'm weird.

I hear teamviewer has a lot of vulnerabilities. They seem to know it considering they have an installation option that completely nukes it after that one use of it.

had, past tense. but nothing will protect you from a zero day and it applies to all of them not just teamviewer.

I did originally to also but it has limitations which made me move away from it

Use RDP.

This post was edited by Klexmoo on Jun 7 2017 02:43pm

If you run it via RDP, you better have good intrusion prevention software running on that system, as RDP port scanners are rampant.

Cyberarms IDDS is a good free option (they used to be a paid software, but now offer the software for free and support is paid).

https://idds.codeplex.com/releases/view/630061

Search for "Google rdp" I have seen it used on phone to play on PC.

Chrome remote desktop