Specifically in regards to Mawgarn’s Axe which allows defeating a monster when moving through a dungeon area.

Unfortunately Defeat is not addressed within the Lexicon.

Mawgarn's Axe - Choose a monster, for each level of the wielding hero, roll 1d6+1. If you roll lower than the Mosnter's HP, destroy this Hero. Otherwise, defeat it the next time this turn you move into of through its room.