Laurefindel
Legend
Referee is one of the smallest roles the DM has. As a DM, I rarely have to make a ruling or tell the players what the rule is. I do, however, constantly play the world and NPCs(other team) as my team interacts with the players' team. I spend much more time playing the game, than I do refereeing it.
This.
In sports and in all events I can think of, a referee is a judge of the rules, an impartial third party between two (or more) competing teams. D&D isn’t about competing amongst players or other teams. If anything, the DM is the competing opposition. But they also play on the players’ teams. Reducing the DM's role to that of a referee is both misrepresenting and misleading, especially when using sports analogies.
The closest analogy I can find is in gambling; whether the croupier is a player is indeed a debatable question. But when asked what they do, croupiers rarely say "I play cards". I'm a DM, and I play D&D. that makes me a D&D player. This is mostly in virtue of D&D being a hobby.
D&D is an asymmetrical game and the role of DM is different from that of player running PCs. Like hide-and-seek. You’ve got a seeker and a few other trying to hide from them. I guess you could say there are seeking-players and hiding-players. Similarly, D&D has DM-players and player-players.
DMs have a different role from that labelled as "player". While this excludes the DM from the role of "player", it doesn't disqualify the DM from the concept of "playing the game" in the same sense as those filling the role of "player". I don't see a conflict here.