Hello,
my question is about the "unique key" needed for playing various games in multiplayer:
How unique is this key? I have two PCs and I`d like to play games on both of them, and in multiplayer too. So, can I install the game on both PCs with the same key and use multiplayer from both?
Or do I need a separate key for each of them?
If you can use it for both, will there be any mentionable problems?

Thank you in advance.

My understanding is that you can use the same key on both machines, just not at the same time. So you can play multiplayer on whichever machine you happen to be using at the time, but if you only have one key, you won't be able to use one machine playing against a friend using the other machine.

Yup, exactly.

However, if you are talking about LAN play between those two machines, the key might not matter at all, depending on the game. Most of the time, those keys only serve to identify unique players on internet multiplayer.