The glossy papers are paper coated with a limestone powder and/or chalk , so it is still a real paper, with the fibrous material (with standard paper the wood, with the asbestos paper the asbestos filaments,...) being the main component. The white dust (either the limestone, chalk,...) then just fills the space between the filaments, so makes the surface smooth. Because the filament structure is still there, the surface could be still soaked with the ink, so the ink can adhere well.
This "stone paper" is a limestone dust filled HDPE plastic foil, which is smooth like any other foil, so the ink can not soak in. It then depend on the ink nature, if it is able to dry on the surface and still form the colored layer.

Seems like you can't get asbestos paper anymore. It would be interesting if there was asbestos paper for photo printing.

Seems like you can't get asbestos paper anymore. It would be interesting if there was asbestos paper for photo printing.

The main use for an asbestos paper was as a material for heat insulation or so.
The only one I've seen was grayish/brown rather thick "cardboard", it was decorated by embossing, but still nothing usable for any graphic work