isn't it illegal to tax interstate goods?
My understanding is that this is a gray area at best. For example, Amazon has to charge sales tax in states where it has a physical presence, regardless of where the item is being shipped from. Since I live in New York, I get charged tax by Amazon on my purchases, even if I'm receiving an item shipped from one of their warehouses in Tennessee. I don't think I get charged sales tax on the marketplace if the seller is outside of New York though.
I don't know if Netflix has a physical presence in Chicago, but assuming that they do, perhaps the precedent which allows New York to enforce sales tax with Amazon can be used to justify the new tax in Chicago? Alternatively, since the end-user's service address is within the city of Chicago, perhaps that is enough to provide them with the authority to tax the service being provided? If that ends up being the case, people that want to save a dollar a month on their Netflix subscription will just use a different address that is outside of Chicago, but I doubt that most people would care enough to go through the extra effort over a dollar a month and maybe that is what the Chicago politicians are counting on?