Actually, it means if you live in NY you would pay the tax and if you didn't you wouldn't.
This is how online stores already operate, and is why if you live in the same state as the retailer has its physical presence, you have to pay the state taxes.
Other states, such as Virginia for instance, require you to pay state sales tax on any Internet purchase you made that you didn't pay *any* sales tax on -- i.e., if you bought from amazon you have to report it and pay Virginia state sales tax on it.
Why this new NY law is controversial is because Amazon has no physical presence in NY, and NY is targeting a successful company to reap more revenue for its failed social programs.
This my friends is why I'm libertarian, keep the government away from successful business. If I were Amazon I'd say sorry, I'm no longer selling to NY customers (see how fast that law gets repealed). But that would be a bad decision, paying lawyers to get this ridiculous law overturned is much more cost effective than not selling to the state of NY.
I love government and politics. Always in the best interests of everyone.