Maxwell'w demon was supposed to decrease entropy, not increase it. (Increasing it is trivially easy. Do some work.) It turned out upon closer examination it could only do so by increasing its own entropy to the meltdown point.
You are right about the the demon decreasing entropy. I was caught in a mental misfire due to superposition of "entropys" I was thinking information (CE Shannon type bits) entropy, and while dealing with the question which was about thermodynamic entropy -- where the higher energy group bottled in one room will flow over to the lower energy group in the other room through the Hall of the Demon.
Personally it seems to me in social situtations that the flow goes the other way -- maybe we all have a bit of Maxwell's Demon in us.