There are multiple ways in which Mike could have gotten back to the Monster World (powering the door from the outside is shown to be possible in the prequel, Monsters University), but for me the most likely way is that he simply traveled to the nearby village and used an active door to return, in precisely the same way that Sullivan did a few minutes earlier.
Although the Yeti said that it was a three day hike, there's plenty of ski gear in the Yeti's shack that Mike could have used to make the journey more quickly:
We also know from the film script that there's at least two other active doors in the village when Sullivan arrives:
Sulley lies motionless in the snow, the wind howling through his fur.
A child SCREAMS in the distance. Or was that the wind? Sullivan slowly
lifts his head.
Another SCREAM, this one louder than the first. Sullivan's eyes widen.
Through the snow, Sullivan can barely make out a SMALL TIBETAN
INT. SCARE FLOOR George Sanderson leans on his crutch, nervously
trembling as he stands in front of his door with his assistant,
CHARLIE: Oh, come on now, George. I know you can do this! I picked out
an easy door for you, in Nepal! Nice, quiet Nepal.