Yes, if you're streaming data to EU and getting money for that from a customer in EU, then you are exporting goods to EU. It's not "as if the customer went to USA, bought the dvd" (in which case it's a local sale and a customer imports their own personal stuff when coming back), it's an international export sale, you bring that "DVD" to Europe. It's as when you ship physical goods through customs, and both the goods and the money flowing through them are subject to EU rules.

If you have zero establishment in EU whatsoever, fines could be taken from all your EU sales revenue (i.e. any funds en route from EU customers to you), and it could be expected that (after they smooth out the process) they also might get a local (e.g. USA) court ruling to enforce that debt on you, there's a lot of international cooperation between the authorities in regards to enforcing trade law. That will take time, though, so until that you're safe unless you want to take money from EU customers or sell the user/advertisement information to EU (or compliant) businesses - in which case, you'll rather want to be compliant.

As a company with a website, there is no obligation for you to serve customers from around the world. Just restrict yourself to customers within a certain region (e.g. by checking where their credit card is registered, or geoblocking based on IP if you don't take payments) that does not include the EU and you don't have to care about EU law.