If you see an error like this:
Failed to initialize the Steam API: Failed Generic(”No SteamClient021")
This indicates that you have an outdated Steam installation, and it lacks support for the "SteamClient021" version of its application programming interface (API). Normally Steam auto-updates, but something must have gone wrong with that.
To check that this is indeed the case, in Steam, at the top of the window, can you go to the "Help" menu, and then "About Steam". It should open a window for you, and at the bottom it should have "Steam API version:". If it's not "SteamClient021" (or greater), it's indeed outdated. Games using outdated versions of the Steamworks SDK will just happen to work.
Try using the "Steam" menu in the top-left corner of the window, and then "Check for Steam Client Updates..." If that doesn't help, then a Steam reinstall should.