Not much!
Their previous game CrossCode has a web demo, if you want to inspect it. https://www.cross-code.com The source code for Alabaster Dawn's demo is also very browsable if you download it on Steam and take a look.
They use WebGL, of course, so there's not really any difference to achieving an art style like this in a browser or any native game engine. Just lots of 2D+3D realtime graphics work.