It would appear that this isn't an analog camera at all(in principle, one could use an optical splitter to put both an analog and a digital imaging apparatus in the same body, with both units afforded the same field of view, lens, etc. but the fact that you can review and even edit before printing, as well as reprint, obviously implies that this isn't how it is being done).
What doesn't seem to be mentioned; but would be interesting to know, is the mechanism by which the analog prints are produced. Typical 'just graft a printer on' jobs tend to favor dye sublimation onto photo-y paper; which works well enough but doesn't involve any 'film' at all in any meaningful sense. The other option, mostly used by larger scale printing services to produce prints that very closely resemble the photochemical stuff; because they are; involves using the digital image to drive a display or RGB laser system(like the "Lightjet" devices) to expose actual film; which then gets developed normally from there.
If this 'Instax Square' format is just obnoxiously expensive bundles of paper and dye-sub strips, it's not very interesting. If they've managed to cram a film exposure based printing arrangement into something of this size and price; I'm not sure that I see the point; but it would undeniably be technically impressive. Unfortunately, no information appears to be available on how the 'square' format film works, as yet.