Thanks for considering our sale.
FM and FM Touch are different games, but that's irrelevant to your question I think.
As far as I know, Steam has a simple check when you sign in to your account from 2 different computers, and will show you an alert about having to sign you out from the 1st location.
According to the relevant article on Steam's Knowledge Base:
Family and guests can play one another's games while earning their own Steam achievements and saving their own game progress to the Steam Cloud. It works by granting family members access to games on a shared computer.
From that I get the impression that family share will only work as intended when using just one computer.
What definitely works, if you wish to play on more computers at the same time, is set your Steam to offline mode (make sure the game is installed and opened once before doing that).
Hope this helps.