He is marking, of course. There doesn't need to be another dog resident for him to be claiming territory
Is he neutered? If he isn't, I'd suggest you get that done immediately. Once an intact male starts marking
inside, it is not an easy thing to stop. At a year old, he's only an adolescent, so neutering straight away will give you a good chance of successfully stopping it.
In the shorter term though, stop letting this dog off his leash at your boyfriend's house. He obviously cannot be trusted. And until he can be, you must not allow him the freedom to roam. He needs to be close enough to you at every moment that you can control his actions - which includes
stopping him, should he lift his leg. In fact, you've got a prior sign of that about to happen, and that's all the wandering around sniffing

Stop him at
that point.
Incidentally - you've posted in the past about your boyfriend's boxer (different person?) and also about a friend's dog that would get excited and pee at other people's houses. No chance either of those animals pee'd at your boyfriend's house? Well, even if they didn't, your dog has - you (or he) need to clean VERY very thoroughly to get the smell out. It's much harder to stop additional peeing when the dog can clearly smell where someone (including himself) has pee'd before.