The Predators drop the group on the moon
This is addressed in the movie where Noland tells the others about it:
NOLAND: Far as I can tell, a game preserve. And you and I are the game.
ROYCE: They do this just for sport?
NOLAND: Oh, yeah, they bring in fresh meat season after season. I mean, shit you wouldn't believe. Bring it in, and hunt it and kill it. ...
Based on the summary from the film's page on Wikipedia, the Predators themselves are responsible for abducting Royce and the others to the Game Preserve Planet.
This is outlined by Noland, who arrived some time earlier, when they encounter him
The group encounters Ronald Noland, a solitary American soldier, who has survived on the planet for "ten ...