Games to simulate community tournaments with?

You can do hands off with the games from Paradox. Stellaris might be a good candidate, as it's the only game where all empires are supposed to start in a similar position.

Advantage: Up to 30 (IIRC) can compete in one game.Good entertainment factor if you report the status quo of the ongoing game.
Disadvantage: It'll require some time till a winner is chosen.

Many fighting games have some form of tournament bracket in-game, but the one that immediately comes to mind is Smash Bros.

Dota 2 and CSGO have full bot support. You can create a custom lobby and have it use AI controlled bots only, then they will play the game as normal. In CSGO real players can also join the server (if you set it up right) and spectate the bots without participating themselves, not sure if you can do so in Dota. For CSGO you can edit the match length as well, since normally it takes 40-60 minutes which can be quite long.

Golf With Your Friends! I just achievement hunted it, you can use all sorts of settings for playing and a scoreboard is displayed for every hole.

Bump!
Just wanted to add: The game itself does not need to have a tournament mode, just a CPU vs CPU opportunity, I can register the tourney in a spreadsheet. :)

any fighting and sports game has a cpu vs cpu mode. Although I think tekken 7 for instance, doesn't have cpu vs cpu but it does have a built in tournament mode with brackets and all

Virtually any classic Worms game. You can even manually build teams consisting of your community members avatars, customize them in many ways. Second coming to my mind would be the Sims games with mods and some creative thinking...many options for some wacky tournaments, not the straight up "harder, better, faster, stronger" ;-)

Rocket League should have full CPU vs CPU functionality (along with Spectator mode functions) and, while the CPU is still massively underperforming in Casual multiplayer modes, after updates maybe a half year back the Custom mode bots can actually be passably functional in their play at their highest difficulty setting. That said, I don't recall if you can customize which bots spawn or not, which may limit you on being able to have your community select representatives to back before a match begins. Similarly, RL has tournament functionality but, well, I also don't know about what options you have as far as customizing that for bots.

Hoser Hockey has CPU vs CPU mode and it's currently in a bundle.

Civ 5 and 6 can run as CPU vs CPU, there is even a channel on youtube that uploads such matches (speeding them up to fit 5-10 minutrs)

Brawlhalla is a good F2P game on Steam.

https://www.youtube.com/watch?v=qgvdPJzUHgM

https://store.steampowered.com/app/291550/Brawlhalla/

I think in Little Fighter 2 you can set up CPU vs CPU matches (up to 8 players).