There is a degree of empathy and understanding, particularly for sports which I’ve participated in. For example, if someone scores a goal on an amazing shot, I know exactly how difficult that was.
There is the drama and artistry of the unfolding event, as mentioned by others here. There is a poetry of motion and atheleticism in many sports, not just ballet, gymnastics, etc. This often equates to a sort of “Wow” factor. My children were enthralled watching gymnastics, both men and women’s, in the last Olympics. It’s no different in that regard than watching a street performer do tricks that we can only imagine doing.
But they also got into the “Patriotic” angle. They’ll ask who is playing in a game or competing in an event. If it has some sort of tie to them (like Cincinnati playing in football last weekend, since they were both born there) then they are more apt to be interested in the score. This is a tie to they’re own very limited past. They cheer for the countries they know in the Olympics. I don’t ask them to do this, they just do.
I wouldn’t dismiss the connection that GorillaMan references. If you grew up in Pittsburgh then the storied football teams of the 1970s are drilled into your psyche. Ditto New Yorkers and the Yankees. There is a sense of association for most people from Boston and the Red Sox. Montreal hasn’t won a championship in years but they are synonymous with hockey. For the English it goes back more than a hundred years for most of their football clubs. Likewise many Cincinnatians still take the day off for MLB’s Opening Day. There is still a parade downtown to commemorate this.
There is also, for many people, a sort of “comfort” to sports. I grew up as a kid watching football with my father. A football game today still takes me back in a way to my own childhood. I had four brothers and sisters, and my father was often away from work or out late. So the some of the best times of my youth were spent tucked in at my father’s side as the Oakland Raiders played the Kansas City Chiefs in the late 60s and early 70s.