Mechanic of switching dimensions is great and I liked it, but I wanted to look up for some reason and was only able to navigate with keyboard like in the good old Wolfenstein games :) It would be good to have mouse support as well. Also, music was coming in 3D from that radio only, for me, some BC music would be better.
Overall, nice experience.
ps. you have a bug. If you collect the Dimensionator and go back to the left wall, you go through it and fall to the abbyss. Add better colliders to walls :)