im not saying anything complex like american football or reg. football but ancient sports that civilizations played (wrestling, gladiators, running,) maybe if you become a city or higher and had a stadium dwarves from other places would come to compete against you and each other. Or even have nobles and dwarves watch the sports
Running: you make a track and have dwarves run across it, first to finish line wins, simple
Wrestling: you designate an area for wrestling and dwarves will wrestle, they would not break bones, instead, they would inflict pain by locking their opponents bones, no injuries would incur (throwing is made safe somehow,) to win a dwarf must throw a dwarf outside the area or make the loser yield (from pain or something) or have their opponent pass out.
Boxing(not very so): designate an area, dwarves would attempt to punch or kick an opponent (in the head if possible) until they yield/pass out. Biting or scratching is illegal
Gladiator: you designate an area, to pit hostile against hostile, (although you can't make people from same civilization fight each other, or animals of same race,) or dwarves condemned to hammering, they become a gladiator and don't get hammered, but condemned dwarves CAN fight each other, you can set teams, you can only make sentient beings on a team, and animals of the same race are forced into a team, you can give people weapons and armor, if someone escapes they can invade you fort, so you should make it enclosed
Not so sport stuff:
Spectators: you can designate rooms with a chair next to sport area, dwarves will sit in chairs and watch the sport, and can get a happy thought, if there are no chairs available that have view of the whole sport area they will sit on the ground, and get less of a happy thought, if the players are unskilled they don't get as much of a happy thought. To sit in a chair the dwarf must be able to see the sport dwarfs with ease.
Schedule: you can schedule training/playing times
other dwarves: sport dwarfs in other nations or in your nation will come if your rep of of good you are is high enough, when sport dwarves come spectator dwarves come. When the economy is active said dwarves will go to shops and buy stuff which giving you coins, while they do bring food for themselves, (a wagon full) if something happens and they are forced to miss the caravan of sport dwarves they will stay at your fort (they do eat food, but do jobs) until another dwarves caravan comes (sport or trader) and will leave with them. If someone dies by anyway, dwarf traders will give you higher prices for a while, when a if a dwarf has never gotten to the safety of the fortress them getting killed doesn't count