There are many differences between this universe and the universe in the show. The most obvious of course being how vastly different lifeforms are in biology, but also in events that have taken place, and how those events played out. Different wars broke out, different wars prevented. Many people’s lives have played out entirely differently.
One of the smaller differences is in Benjamin Sisko’s favourite sport. Whilst Baseball fell out of fashion and play by 2042 (DS9 If Wishes Were Horses), Basketball is still played in the 24th century (shown in the 22nd century in ENT), which is no doubt because the way the game is played allows for a wide range of non-humanoid species to play it too.
In 2375, Captain Solok of the USS T’Kumbra challenges Captain Sisko to a game of basketball, and the Niners team is formed. Vulcans have a reputation for being especially good at basketball (if they choose to play), since their telekinesis can allow for extreme accuracy.
The Niners starters consists of Ben, Jake, Kira, Asha and Julian. Substitutions on the bench include Nog, Leeta, Rom, Quark, Kassidy, Miles and Keiko (not all necessarily as enthusiastic at the prospect of playing). Cheering is provided from the seats by Jadzia, Ezri (if the Trill could play, they would) and Worf (whose cheering is more roaring). Sneering at the whole affair is provided from the seats by Garak, whilst he provides morale support for the still-recovering Ziyal, who really wanted to be there.
Probably more goofy cartoons of this to come. XD