This is based on a law that was recently passed by the New York State Legislature. Typically, in order for a state to be allowed to force a company to collect sales tax on its behalf, and not be in violation of the "taxation without representation" precept of this country's Constitution, that company has to be based in the respective state that the tax is being collected for.
About 15 years ago, states started forcing companies to collect sales tax on their behalf, even if they only had a "presence" in their state. Unfortunately, these rules have been upheld by certain court decisions.
The new law passed in New York, extends the definition of "presence" to include a web presence, and to include the web presence of an affiliate or otherwise related entity. That is why Amazon, for example, has to start collecting sales tax from New York customers. Even though Amazon is not based in New York, has not physical presence of any kind in New York, they do have "relationships" with other booksellers that sell through Amazon that DO have a presence in New York.
Needless to say, Amazon is taking this to court, to try to have the law overturned.