DM = Dungeon Master. But like in this kinda setting it's Dungeon Master and Game Master are interchangable.
I've only been reading what manga gets translated, haven't touched any other source material. If I had to describe the Gods (DM's/GM's) in Goblin Slayer, I'd say it's like a bunch of really bored assholes got the idea of the pen&paper dice RPG games from somewhere and decided they were gonna manipulate events in the mortal realm with the results of their dice rolls and use that as proxy to their own conflicts.
I say it like that cause Goblin Slayer basically sets things up to consistently counter as much as possible anything that can be or has been influenced by God's dice. It's like a big part of his GS's core concept/theme,