In order to play *any* game bought from Steam, the Steam client must be running and have an internet connection.
This is incorrect. Please stop spreading disinformation and/or stating things as facts that you have done no research or testing on.
Yes, there are some games purchased from Steam that require the client to be running in order to load the game, even in "offline" mode. However I have multiple games in my Steam library that do not require the Steam client to be running. I manually start up the Steam client only when it is needed and leave it off the rest of the time and have no problems with certain games.