The final version of Greg changes his Level Up Ability to apply only to Ordinary Monster Rooms, not Advanced Monster Rooms.
Greg's Level Up Ability works in a dungeon set up oriented towards the building of Monster Room cards, as it can give a boost to any Ordinary Monster Room the player builds later on.
Greg appears to be a type of monster similar to King Croak, albeit much thinner.
Below is an excerpt from the Boss Monster: The Video Game description of Greg as a character, and the gameplay style:
ABOUT GREG: His full name is Baron Gorblegreg the Ravager, but your new Boss just wants you to call him “Greg.” After all, even though his responsibilities as a Dungeon Regional Manager keep him busy, Greg’s door is always open for his minions. Just don't get on his bad side when it's time to climb the corporate ladder, because Greg thinks he can do things better than anyone ...even King Croak.
GAMEPLAY: Thanks to his cutting-edge management techniques, Greg keeps any Monster Rooms in his dungeon operating at maximum output. In-game, Greg’s Level Up ability has the potential to take your dungeon’s Damage to new heights. However, the ability requires you to focus on Monster Rooms, and doesn’t apply to Rooms you’ve already built. Other Boss abilities come into play more quickly, but in a long game getting the maximum of five +1 counters can free you up to focus on lower-damage, higher-treasure Rooms.
For the rest of the game, whenever you build an ordinary Monster Room, you may give it a +1 counter.