Here, we have 2 reasons that Paterson and the New York State Assembly/Senate got involved:
1) There is a legitimate public health concern with running unlicensed hotels -- subletting your 2 bedroom for a couple months is one thing, renting places in order to run a business out of them while circumventing health regs that are there for good reason is something entirely different. They were seeing a shift to the latter.
2) Simultaneously, hotels have money, have lobbyists, didn't like this and had a great argument to make with public health. The senator in question can keep the donations flowing while all the while claiming he's only concerned about the public welfare.
So, some mixture of that is what happened. Notice how none of it involved Glenn Beck's nightmare socialist conspiring to reduce "freedom" and expand "government" in order to, you know, piss off Glenn Beck or whatever motivates all of those socialists. When you unpack political reality, it turns out to be a lot less about "government vs private sector" and a lot more a combination of who has the money (usually one aspect of the private sector).