That version of "Doom" isn't actually Doom at all. It's actually just a clone of Wolfenstein 3D with a few graphics from Doom.
What this news post is about is actually quite impressive, however. Unlike that shoddy excuse for a "Doom port" above, this new port is actually a full port of the original Doom engine running on a graphing calculator, something that to my knowledge has never been done before. Thus, what you see in the video in the OP is actually Doom on a graphing calculator, unlike the video above which is just a Wolfenstein 3D-style raycaster engine with Doom assets.