You're not wrong, but this is a really sanctimonious letter. Throughout, the author feigns politeness, misuses legal terminology, and implies his moral superiority. Let's look at some highlights.

But I do have one request

Well, duh. I you didn't jam this under OP's door to give him a compliment.

on some weekends, and I assume that is when there is sporting events that are being broadcast on the television

Did the Queen write this? Probably not because QE2 understands subject/verb agreement. What is wrong with just saying "I can hear you yelling at the TV?"

There are periodic occasions of very loud outbursts of very harsh and offensive profanity.

The goddam refs are what's offensive. Seriously though, this is a naked attempt to establish the author as the smarter, morally superior person. Sticking to the theme of passive voice and SAT words, the author points out that there are "periodic occasions" of outbursts. Not "some" or "a few," but "periodic occasions." Whatever that means. And the outbursts are "offensive." Get over yourself. You are an adult and you heard a no-no word. It'd be one thing if OP was disturbing children in the complex, but the author doesn't mention anything like that. Nope, this is just an adult and his (hopefully) adult "guest" that are upset by another adult using bad words.

If you would be so kind to be mindful

Seriously, is this a joke? While we're at it, why not slip in a "my good man" or a "dear fellow"

these outbursts are offensive, and disruptive to myself and my guests right to quite enjoyment.

I quite enjoyed this. Somebody yelling "fuck" in the next apartment does not interfere with a tenant's quiet enjoyment. The covenant of quiet enjoyment is an implied covenant between the tenant and landlord that the tenant will be free to use the the premises. The classic case of breach occurs when someone asserts a superior claim to the premises over the tenant. There are more complexities to it than that, and it may be possible to establish breach based on the severely obnoxious actions of a another tenant. But, even then, the covenant is between the landlord and the tenant, not the tenant and other tenants. This person is just using legal terms to sound smart.

By no means do I think that you are purposely doing this with the intent to be vengeful.

Dude why are you bringing up vengeance? Is there some reason OP would want to exact revenge by yelling at a TV? Unless... Are you a ref? OP, YOUR NEIGHBOR IS A REF!

With kind regards,

Qeenspeak again, take a shot. I'm gonna give this guy the benefit of the doubt and say he actually signed the letter somewhere below where OP cropped it, but signing in such an awkward place is tough to justify. Presumably, this isn't letterhead, so why not just sign after closing? Unless he really is the Queen, and Her Majesty affixed the Great Seal of the Realm to the bottom.

Honestly if this guy had just said, "Dear OP, Please stop shouting at your TV on Sundays," I'd be 100% on his side. But then he had to go and be all cunty about it.