Really depends on your definition, but by most online consensus and generally by most definitions I’ve seen, a DM can indeed metagame. If you personally don’t feel that way, that’s fine, but a DM is considered a role player in my experience so the following definition holds:
The act of a roleplayer making use of knowledge that they have learned out of character (and which their character does not know) while they are in character
If I have a random shopkeep tail the rogue of the party through the shop, even if their character does not give off rogue vibes, I’m being metagamey. I know they’re going to try something so I use that to change the behavior of the shopkeeper. To me and to most other people according to a quick search, that’s metagamey. You can feel differently, but I believe that puts you in the minority.
The DM can not metagame, definitionally
Really depends on your definition, but by most online consensus and generally by most definitions I’ve seen, a DM can indeed metagame. If you personally don’t feel that way, that’s fine, but a DM is considered a role player in my experience so the following definition holds: The act of a roleplayer making use of knowledge that they have learned out of character (and which their character does not know) while they are in character
If I have a random shopkeep tail the rogue of the party through the shop, even if their character does not give off rogue vibes, I’m being metagamey. I know they’re going to try something so I use that to change the behavior of the shopkeeper. To me and to most other people according to a quick search, that’s metagamey. You can feel differently, but I believe that puts you in the minority.