They’re not. They are using BGI’s MGISEQ2000 machines. They simply sell the sequencing at a price that doesn’t cover its cost. Both because this is a promotion and because they retain the rights to using your genomic data in research: it’s simply a cheap way for them to get samples.

DIY microfluidics is possible with shrinky-dinks circa 2014; but for-real genomics is a little harder TBH

Is there anything more to it than carving a piece of silica and ligating the adapters to the surface? I mean, I know the process is a bit more involved than that but the patents make it seem relatively straightforward.

It's straightforward in a conceptual sense, but as with most things there are a ton of gotchas and fiddly implementation details, especially if you're doing it in your kitchen/garage. A lot of the difficulty comes with the tedium of maintaining sterile conditions and lots and lots of pipetting.

If you're really interested in DIYBIO there are subreddits and many tuts out there, but fair warning: getting started is easy, but the devil is in the details a heck of a lot more than learning to code.