Apparently the newest version of GOG Galaxy now schedules game updates for installed games not actively played, which I believe means the client checks if a game is being played before being updated. However, I only use the GOG Galaxy client for keeping all my games automatically up to date, and I prefer to play everything offline outside the client and have all game features disabled in settings except Auto-update games, so none of my games may register as being actively played.

Is there anyway to disable scheduling game updates for installed games not actively being played or do I indeed need to start playing my games through the GOG Galaxy client with Game Time Tracking enabled if I want to continue to receive automatic updates?

If you installed a game using Galaxy (or even added to it after the installation), the game will always use the Galaxy services when it's played, even if Galaxy is closed, so the local client always "knows" what was played or not.

Unless you manually disable those services after every time you close the client and re-enable them every time you open the client...