I’ve worked for several D1 colleges, closely involved with their athletes. Many of them are pro basketball players and baseball players. Schools in New England that are perennials in NCAA championships. I’ve worked around professional football and the NHL.
If you have never been around them, you can think its a game.
If you have never seen a professional football playbook, with the different defenses and audibles that could be called for any number of situations, I can understand why you think this is “play.”
I also recall Gary Player commenting when asked how his swing seemed so easy, he stated that he bled for hours and hours on the driving range.
Work is work. I am not sure how you would define it. I would suggest perfecting your mind and body to perform at the absolute peak is work, not matter how you slice it.
. You said you are not sure how to define work. That's why you are missing the boat on this. Sports is something we do for fun whether we get paid or not. It's an act that is pleasurable. So is acting or playing a musical instrument.
People don't do accounting or install roofs for leisure. It's not pleasurable, it's "work".