What does Competitive PvE mean to you?

I was watching some videos of competitive raiding in WoW. It's basically a race for the best clear time between the top parties. It's hosted by WoW directly and also has a corresponding cash prize for the winners. I believe they were trying to push this into an esport, but I don't know if that actually took off. Does WoW have other official modes of competitive PvE?

In the game I'm playing at the moment, Tree of Savior has multiple competitive PvE modes. The main attraction right now is the weekly boss raid where a single player fights a raid boss in 7 minutes. There's a leaderboard of players with the highest damage, and the top 10 players for the week gets some nice rewards. Players can also get specific rewards by certain total damage threshold after seven attempts (no need to be ranked). This concept is simple but effectively encourages players to fine-tune their gear and build to become stronger, and a party version of this mode is in the works.

Does your mmo have an official competitive PvE mode? How fun is it?