The use of the cartographer to generate separate designs and the technology used to render/deliver those designs are two entirely separate concerns.

His original map provider offers both vector and raster tile services: https://www.thunderforest.com/maps/outdoors/

A common pattern is to use a vector tile service + style definition directly or to generate raster tiles if those are desired.

Good point, I assumed he was using images because his screenshots show text perfectly following the curves of rivers, which seems hard to do with dynamic rendering.