Thomas Shey
Legend
Football referee's are bound by the rules. They aren't players. They even make judgement calls that can often seem very arbitrary.
To say it a little more clearly - 'Players follow the rules pertaining to them. Refs follow the rules pertaining to them - rules which typically require them to serve as a player rules enforcer', but sometime the rules may also pertain to how they are required to do things as well.
I think referring to referees as players just because games typically have rules around the referee role only serves to muddy the waters. However, there is a way the GM is like a player (a way that the football ref isn't) and it's got nothing to do with following rules - it's about them playing the opposition.
I realize that this is probably calling-back to an earlier post drawing a football analogy that I skimmed over, but I'm not sold sports refs are a good comparison to GMs; the latter have far more player-like actions they participate in, in the form of the creative elements and things like operating NPCs. I think thinking in terms of them as referees (though in classic usage that's certainly part of their position) mostly muddies the water of the discussion (especially since part of the question is whether their refereeing element being unique to them is actually necessary).