I do not have any specific knowledge on our problem, but as there have been no responses I assume those with more experience can't comment even after your good effort to "draw a picture" with words.
My experience with humans with deep cuts, haven't had the experience with any of my dogs, is they need a stitch (maybe glue? - I don't know the latest) or two to close them for proper healing. It sounds a to me that is what was needed in for the subject dog.
I say better late than never, if the wound doesn't look good, take the dog to the vet, as is also said, pay me now or pay me later - later is usually more expensive and painful.
My dog got a paw pad cut a couple of days before your roommate's dog did. What I know now is that what it looks like at nine days is not what it will look like when it is fully healed. It's been almost a month now, and you can't even see where it happened. But nine days out, there was a ridge on the paw pad. Sorry I didn't know this at the time you posted. I hope your roommate's dog is alright now.