But I mean you can 'make up' new content. That's literally what they do for 'fake 3d'! They 'make up' new background content for areas uncovered by the shift needed to create the parallax, using either machine estimation or manual drawing. How else did people think this worked?

Yeah, the page is a bit disingenuous, and they're all affiliate links.

You need a depth map to compute parallax.

Yes they make one using simple models that roughly fit the geometry on screen. Then transform for parallax. That may reveal hidden areas so they fill them in either using an algorithm from surrounding areas and recent frames or manually.