The toymaker isn't magical or scientific, he isn't bound by our rules or logic. he's toyed with supernovas, turned galaxies into spin tops. he gambled with God and made him a jack-in-the-box. they made a jigsaw out of the doctor's history. (Did he like it?) The Master was dying and begged for his life with one final game, and when he lost, the toymaker sealed him for all eternity inside his gold tooth. There's only one player he didn't dare face. The One Who Waits. because that's someone else's game
He's the god of games one of the pantheon, they never originated from this universe and came to spread chaos. and although they can be beaten it's never permanent, and one trick is all you ever get for them and the toymaker is no different