Board Game Arena

What game on here is the quickest to play? If I have only 10 minutes, which game would you suggest?

If you only have 10 minutes, I'd recommend setting up a turnbased game so you can come back to it if you don't have enough time to finish.

Unless you're playing with friends, you can't ever guarantee your opponents won't take a bit too much time to act, even on the shortest games.
However, for games like Martian Dice, Conspiracy or Pirate Kappern, as long as you don't put too many opponents, the game should go fast enough.
Draftosaurus would probably also be a good choice, as well as Incan Gold, as those have all players acting at the same time and a rather low amount of turns.

Battle of Lits is very short too. Same for Insert. Go Nuts for Donuts if only played with 2 - 3 people.

When I want a quick game, it's between Insert (beta), Draftosaurus, 7 Wonders duel and Conspiracy. Elimination games like Shrodinger's Cats or Coup can also be very quick !