I think there might be a difference between "having fun" and enjoying playing pool.
While I"m not a pro player, I do spend a lot of time in the pool room.
When I walk into a room, see a friend, and we decide to do a little sparring, I usually have fun. It's about playing, enjoying the company of a friend, a little friendly sharking and trash talking.
When I am in competition, either in league or in a tournament, my mindset changes. I look forward to my matches, not because it is fun, but because I enjoy the opportunity to put my skills (of lack of) to the test. I enjoy the atmosphere, I enjoy performing, and yes, when it comes together, I enjoy winning. I would not say that competition is "fun", but it sure is enjoyable.
Steve