I think that an option to spectate a match even after you have left it would be useful and a spectator count in the corner so you could see how many people outside of the match or defeated are watching.
You could have an area for watching match replays that you have recently played in and options to save them. People could search other people’s users and watch their recent matches.
You could have a featured section that can show selected matches that may be interesting for people to watch. It would be nice enough at least to have a view count and an option to rejoin/watch matches you have been in and have just left.