So I was recently looking through my games library wondering why it was so small and then i remembered having played a few on my last computer that weren't showing up in the library.
I went to the DOTA 2 page on steam to add it to my library, but to my surprise it showed up as "In library". However, when I went to my library, it wasn't there.
Best Answer
Free to play games that you haven't spent money on will disappear from your library after they're uninstalled, but Steam will keep track of the time you've played them and mark them as "In library" on their store page.
If you have spent money on a free to play game, on the other hand, when uninstalled it will still show up in your library as a darker shade of grey, like games you've purchased.