You don't actually own the license to F2P games, but they are counted in your game total.
F2P games don't count towards your main Steam Community game count at all, with the exception of F2P games you added to your account before they were added to sub 0 (e.g. Dead Island: Epidemic). If you have play time they'll show up in your All Games tab and if you own DLC for them they'll be tethered to your client library in much the same was as they would be if you'd bought them, but that's it.
Edit: Did anyone else receive a copy of Hive at some point within the past ~9 hours? It wasn't a gift -- it just appeared in my inventory as a new item.