Wait, how do these interdimensional doors work!? Is it the work of the gods?

Yep! A Fox spirit in particular.

Nobu's is a fox spirit (Kitsune), related to a specific god: Ukanomitama, who is associated with food and rice. We learn this when Efa gets lost in Tokyo and the fox spirit that guards Nobu mentions the god's name when sending Efa back.
The other door is theorized to have been the work of a Tengu due to a myth from the man's hometown.