Do I have to install a game to keep it, if it is free for a limited time?

I am asking this because Outland is free until tonight on the Steam store and if you get it is permanent. However, due to internet restrictions, I can't download it right now. However, I managed to open Steam and click "Add Game" from the store and I then went to Outland's page and clicked "Install Now". Then it took me to the page where it said:

Thank you for purchasing Outland, it has been installed to your steam library

Then it said to click a link to install it, however, I don't want to currently. So if I just add it to my library is that enough to claim it or do I have to physically install it to my PC?

Provided you have added the game to your library while it was free, you will be free to download it whenever you like. You can also download it onto other devices too (via your steam account).

Yes, once the game is in your Steam Library you get to keep it regardless as to whether or not you installed the game on your PC.

When you clicked "Install Game", Steam registered it to your account and provided you with a game key similar to the ones you get from the Humble Bundle or when you purchase a download code from a brick and mortar store. That game key is what signifies your ownership of the game and it's virtually linked to your account now.