How do you get to play darts against the other player on cryptids island?

You have to leave Loch Ness with the "loops" photo and come back.

There are two players you have to beat. The first one, with the mustache, has the rowboat ticket. Once you get the photo on the rowboat, you return to Mews.

When you go back to Loch Ness, you play the man who has the submarine ticket. Get the photo and bring it back to the pub. You will now play the first player again.