Is my dog marking his territory?

It could be a number of things. Marking territory? Perhaps. Simply peeing due to still being able to smell it is another possibility. It could also be caused by general anxiety when passing through that area. I'd make sure to get an enzymatic cleaner like Nature's Miracle or a water/vinegar mix. Regular soap and cleaner does not cut through the smell - dogs will still smell it and continue to go in the same spot.

im confused on what your bigger concern here. Is it that your dog is peeing in the house where she wasn't before? Or are you looking for reasons to build a case for your friend to use a different mop? It seems to me like that's the bigger concern here.

If it's the latter, I don't think marking is very convincing. To your point about the dog marking it's scent because of where the mop is being used- If that was the case your dog would be trying to pee on the mop itself, or in other areas around the house where messes are made. If your dog was marking, it would mark different things it "owns"(probably things belonging to you or new items brought into the house) and not just that one spot.

Look for patterns in the accidents and when they occur. If my dog has an accident while I'm not home, he also goes in front of the door. I figure it's because that's the closest spot to being "out". I'll admit those times are when I've left in a hurry without making sure he properly did his business outside, but if you're doing your due dillegence with potty breaks, consider contacting a vet about bladder issues. Maybe your dog can't hold it and waits infront of the door to be let out until an accident happens.

As for the mop situation, just explain to your friend that it's unsanitary and damaging your floors. Show them how you prefer messes to be clean. If they're a respectful roommate they'll understand.

Dogs will pee where other dogs have peed, plain and simple. It is about territory but also that the area now smells like a toilet to their very sensitive nose and dogs being creatures of habits, they like to do their business in the same place.

So yes, soaking up the urine before mopping helps quite a bit, using an enzyme based cleaner or adding vinegar to your mop water also helps but really the solution here is to ask your roommate to get his dogs house trained since no matter the amount or type of cleaning, constant peeing on your floor will ruin them.