Tournament - poll.

Coliseum + random + abominations?

I used to play a browser game called "Gladiators," and it sounds very similar. Abominations sometimes appeared there if a mounted gladiator lagged, and there was plenty of coliseum and randomness.

And the developers seem to have made or are planning to make a special multiplayer client for "Horn of the Abyss."

I think they already did, and there's also some kind of lobby for SoD (with the HD mod). I don't play myself, and I rarely catch the beginning of streams, so I might be wrong.

Added 5 minutes later

But everyone has Steam and licensed copies, after all, we're living in 2018.

I have about 5 licensed games on Steam, and they're not even the most popular ones.