You're right. But even if he didn't have them, he was still staying there as a guest of the legal tenant. The story doesn't say there's no lease or that an eviction had already occurred. His cousin had a lease but no longer lived there who was there as a guest of the leaseholder/unauthorized sublease and they were going to evict the guy still living there. There's still a requirement to go through eviction proceedings in order to legally terminate the lease and classify the guy living there as a trespasser. And even that doesn't warrant going in with friends to shoot him or threaten him at gunpoint. It just means the police can remove him.

In short, the situation was pretty ironclad grounds to terminate the lease through eviction proceedings but he was not a legal trespasser at that point nor was the landlord justified in an armed breaking and entering.

Adverse possession is completely different matter than establishing tenancy…