There are plenty of opportunities for sports on Santorini. Windsurfing, Sailing, Swimming, Beach Volley, Basketball, Football, and Hiking are some of the sports you can easily do on the island.
Horse riding and Kayak are some other sports you can do on the island. For more information ask at a local travel agent about 'Naturaction' which is the organisation that arranges this type of activities.
Donkey riding is not a sport really, but I thought I'd mention it as another thing you can try on Santorini. You can use donkeys to go down to the old port from the town of Fira.
Football is also another sport you can enjoy. Just visit the football stadium at Kamari to either see a local football match or simply gather your friends for a friendly game.
If you are a fan of water parks then it may be a good idea to visit the 'Water Park' or 'Wave Sports' located between Perissa and Perivolos. Alternatively if you like things like diving, snorkelling, etc you should go to the 'Mediterranean Dive Club' or the 'Santorini Dive Center' at Perissa.
Beach Volley and Rackets are some other very popular games, that you can play on the beach. For instance, on a swimming trip to Perissa, Perivolos or Kamari....keep an eye for the designated beach volley areas, where you can go and play with your friends. Alternatively, if someone else is playing, you could ask to join them...and you never know...you might make some new good friends or very simply have a great time.
In plain English....there certainly are a few opportunities for sport on Santorini.