The re-releases of Doom do use the original Doom, alongside Unity. Here's where we get into Theseus' ship: the game logic engine itself is still original Doom's, but Unity is used for the video output, sound, and input engines, allowing for easier ports because of the difference between console and phone graphic APIs and input options.

https://doomwiki.org/wiki/Doom_Classic_Unity_port#Architectu...