It was a very dark, cloudy night, and they were a bit late arriving at Hagrid's hut because they'd had to wait for Peeves to get out of their way in the entrance hall, where he'd been playing tennis against the wall. (Harry Potter)
In the example, a participial construction seems to modify an adjective, late. Can a participial construction have the same function as a to-infinitive does, or does this have the role of something else?