Why would these two Dune characters get married?

Agree with previous answers that it was definitely for political reasons, as Leto II hardly thinks about anything but politics and his Golden Path (clearly intertwined) by this point in the book. It was definitely due to a mixture of political motives, many of which have already been mentioned. I'd add that it was also was an attempt to appease the Bene Gesserit, who ultimately wanted them to have children together. By marrying Ghani, they'll have a hard time telling him to do something he's "already done".

It's been a number of years since I last read Children, but bear in mind that well before the end of the book Leto has already embraced the Golden Path (to preserve the future of humanity). So any action that Leto takes is primarily intended to further that.

Also, Leto is already beginning his transformation, so it's highly unlikely he could have children of his own. By marrying Ghanima, he makes her children (by whatever father, most likely Farad'n but it doesn't really matter) officially his. In doing so he removes the chance of a blood heir of Paul, but not Leto, arising who might challenge Leto's rule.

(Note that in the Dune universe it is clear that marriage is a purely political union, distinct from whom one might love and even who one's official heir might be. Paul's marriage to Irulan was political; he loved Chani and she bore his heir. Paul in turn was the heir of Leto I, even though Jessica was the Duke's consort.)

But it is for political reasons, like everything else the Atreides do. With either of them unmarried, there would be pressure from ambitious Houses to marry their children. In particular Ghanima would be a target since any children she had could be a political threat. And don't forget that at this point no one really believes that Leto will live for thousands of years.