Given that dad kinda wanted to get the hell out of there before they had sex, and didn't go in the closet even expecting them to use that room (per their dialogue), I doubt his original intent was peeping. Otherwise, the whole "I missed my chance to get out and now I'm stuck in an embarrassing situation" is kind of a classic Japanese comedy trope.
Analyzing it intellectually, it's clear that the purpose of Dad in the Closet(tm) is to perpetuate the chain of comedy that runs throughout the comic. He's just another piece of the joke. And the comic doesn't take place in the real world, but rather in that comedy setting that looks an awful like the real world but really isn't.
Emotionally, I react to the comic as a man with a daughter. My brain pencils me in the closet and her in the room with a potential lover, and I get kinda skeeved. I think you'll agree that it would be cringey as fuck, start to finish, if the events in this comic really happened in the really real world.
For which, see "This isn't the real world, but a comedic variant thereof." I understand that, and don't have a problem with it. The comic is funny! Tamamusi did a great job on it! I can see how other people can appreciate the humor of the comic on its own without getting skeeved. I'm just a little too close to the issue to pull that off myself.