I think the unique advantages of online gambling is like what you describe and yes, I like to play online gambling in my room with secret and I don't want other people to know I am playing gambling. besides that, the other advantages of online gambling, we can play the game without visit the casino and we only need to use our browser to play.
You are right, convenience and anonymity are unique advantages. Another advantage is variety of the games, you have more options in online casino in comparison with traditional casinos.