I haven't seen the film being discussed, nor did I see the stage production that preceded it. Here are a few details I can provide from the original published script. These may be helpful.
Michael lives in "A smartly appointed duplex apartment in the East Fifties, New York, consisting of a living room and, on a higher level, a bedroom."
Perhaps these lines were cut here, but at the end of the play, Donald tells Michael that he will be gone by the time Michael gets back. Perhaps in this film, if those are lines are still there, Michael is running home in the hope that he might be able to catch Donald before he leaves. I don't know.
If I can, I will come back to try to provide more info about various things that have been brought up in this thread.