Yes, he's marking his territory.It is not simply urination out of need. Dogs do not empty their bladders doing this; they simply squirt little enough to mark the spot, and can therefore do it dozens of times without any difficulty . Once he has marked a place he will constantly return to it, to refresh it.
When did he 'learn' to cock his leg? Has he recently learned to be a grown dog?If its a recent 'skill' he has yet to learn that showing off his male attributes and strength is for impressing rival dogs outside ,not you inside !
How to stop it? Practically, you can try to clean the marked spots so he isn't prompted, by the smell, to mark them again. That's only a partial answer, since the question is 'Why does he want to mark in the house in the first place?' Plenty of walks, so he can do it where it counts, is a start. But really, the answer is 1) to watch him like a hawk and yell 'No' and stop him at the first sign of his looking to do it, and put him outside (you have to be quick!) 2) have him with you for cuddles, comfort and reassurance, at all times, so he's happy in himself and distracted. He should gradually learn that he does not need to assert himself by marking in his own home but only outside, where other dogs can smell his efforts.