I reckon it's one of two things. a) The voices. Acting out characters and especially their unique voices I think readjusts your throat to produce all the varying tones, pitches, etc etc.  b) Pressure relief. Playing D&D can be extremely entertaining regardless of how serious everyone takes it. Just relaxing in any scenario seems to do it for me (not always though...) Do with it what you will; I'm not a speech path.