Can two accounts play a game only bought on one account, on the same computer?

Solution 1:

Yes, you can share your games with your family. Steam recently introduced Family Sharing, a system where a user can share his library with the rest of the family and others who use the same computer.

You simply need to enable Family Sharing on the computer you want to use:

1. Log in with the account you want to play with
2. Log in with the account that owns the game
3. Go to settings > Family > Authorize This Computer...
4. Authorize the borrowing account by checking the box under Authorized Accounts

Note that two users still cannot play the same copy at the same time.

Also note that not all games support this system, or have only partial support. For example, you cannot participate in CS:GO's competitive matchmaking while borrowing the game from another account. Most games with 3rd party DRM, such as Uplay, will cause issues and might not even show up on the list.

Solution 2:

I've noticed that some games available on steam will continue to run even if the underlying steam account is logged out for some reason. This can either be from a bad internet connection or from someone else on another computer logging into the same steam account.

These are typically older games that have no steam integration. I know this is the case with Trackmania United.

So it might be possible with older release games or third party games to get by the restriction by lauching the game on one computer, then logging into steam with the same account on another computer. If the game doesn't use steam for finding matches (and uses some other method) than it might work. That being said I am not advocating the 'theft' of games from steam. Particularly since your example game Garry's Mod only costs $4.99 right now.

You could always gift it to her account :)

Solution 3:

I've noticed before that if my girlfriend logs into her steam account on my computer that often my games (that aren't on her account) show up as installed and ready, But she can't launch them.

The actual files will show up in the list as installed and ready to go, But unless your account is authorised to play the game it won't run.

TL;DR - It shows up on the local computer, But won't run unless you pull your wallet out.