I've been dying for an update for this engine. I think what he is doing is rendering these panels with height maps in 2D, then going through and cutting out the 2D image which is scaled to represent various distances. That's actually the way old time blobbers do it but here he is taking advantage of height mapping to produce features on the surface of the texture map. Very, very impressive results from very little image data. I believe he is creating the illusion of movement using scrolling and adjusting the viewport in real-time to make it look like we are zooming forwards. The end result is an extremely impressive emulation of the original 2D crawlers.
I'm pretty sure you're right yeah, I've dabbled in building my own 2D HTML/JavaScript based engines and think you're spot on with the movement. From what I can see he's fading out and in the old and new image but with the zoom used it actually feels like you're moving.
I've also seen some videos on how Doom, Wolfenstein and later 2D simulated 3D engines work and this looks exactly like that, just prettier.
But Sébastien was lead dev on Dead Cells, so I bet he knows some magic. He has a github, might be interesting to crawl through that: https://github.com/sbenard