No, they are not "pushing" data.

Pushing implies that data is sent by the server without clients explicitly requesting it.

Pulling is when the client requests data explicitly.

I get notifications pushed to my phone by Apple.

I pull YouTube videos.

YouTube doesn't suddenly decide to "push" random videos to my phone in the middle of the night.

Similarly, Netflix doesn't "push" videos to their customers.

"Push" and "pull" in this context refer to the initiation of a session. The user is pulling, because they start streaming. Netflix does absolutely nothing by itself - it doesn't randomly start delivering data to you.

Nobody says that a bullock cart involves the bullock pulling the cart and the cart pushing the bullock. That’s only a physics framing.

This is commerce. It's a transaction. Both parties benefit.