Cool. Evidently the family disagrees with you on it being necessary. The fact that the ability to grant an eviction notice is exclusive jurisdiction of the supreme court rather than lower courts implies the state of new york disagrees with you. Given that the article makes it extremely clear that it was the son, and not the parents forcing the legal process, that also implies you're making assumptions.
Evicting someone can be a complicated legal process. If the person refuses to leave, there is quite often little you can do until you get a court order for that eviction to be enforced. "Throwing someone out", is rarely simply if the thrown out party isn't willing to stfu and leave.
here, let's not speculate and break out the google foo.
https://www.google.ca/search?ei=4B8GW9qjNcfXjwTLrrOQBA&q=ejection+action+adult+child+new+york
Oh look, if the adult child pays rent or has been expected to (bascily if there is an enforceable lease), then they count as a tenant and it requires all the proceedings and expectations of that. If they do not pay rent, then it requires an ejection action, which is a relatively through legal process, apparently more complicated than evicting a tenant. Just about every page on the opposite side of that link recommends you retain a lawyer for it,it requires an explicit court order from the New York Supreme Court and can apparently it can take several months and be pretty expensive.
So turns out that the process is rather more complicated than you're blithely assuming, as legal processes quite often are. Congrats, you've managed to be both wrong and a needless prick about it. Where are your wheaties.
Editing rather than double posting:
Some of these liberal states have extreme laws to protect people from getting thrown out in the street. They believe it cuts down on homeless camping in front of Starbucks. I believe this guy was using these laws to prevent his parents from throwing him out. Also these people create these go fund me pages, and real stupid people will actually send them tons of cash. Whatever.
If we go hunting, I expect the law to have been written to cover any ejection of a family member. There have been quite a few cases of abusers and other such bottom feeders using the threat of homelessness to control their victims. It'll be there to help prevent things like someone throwing their spouse out of the house because the title isn't in their name, or pulling shit with their parents/grandparents or just being like "btw , you're 21, and now you're homeless!" without giving them notice or the ability to prepare. I've seen the last of those happen personally, friend of mine got chucked out on her birthday by her shithole of a stepfather. I don't care to research enough to know laws here stack up vs new york state, but suffice to say neither the police nor the courts were amused at him for doing it with no notice in the middle of a northern winter.
Good laws occasionally protect assholes who know how to abuse the system. At least up to the point a judge gets their metaphorical mitts on them and systemically dismantle their bullshit, exactly as happened here.