No, the term "event" applies only to indoor sports. Pub customers playing a casual game of darts isn't an "event", even if it's taking place in public and there are spectators. An organised darts match or demonstration might be an "event".

Like you, I can't see much distinction between customers playing darts or pool for their own amusement, and customers playing music for their own amusement. However the Act does make a distinction. Live music is on the list of regulated entertainment. So far as I can see, the Act makes no distinction between music made by customers or organised music. There's no requirement that anyone is actually entertained by it, simply that it takes place in public (which might include the musicians at a session) and is one of the activities listed in Schedule 3 Part 1 Para 2(1).

I imagine that most sessions will fall within the 100 people maximum for the proposed small events exemption, should it be implemented.