Puppet Master's card text states that it can special summon Zombie monsters from the graveyard, but the actual card in the game special summons Fiends, just like its real-world counterpart.
The Puppeteer of Doom and the Mimic of Doom cannot exist in the same continuity, as they do in this game. The latter character was created as a replacement for the former (a manga-only character) in the anime, which this game is a sequel to.