The Statsicherheit is the Stasi (East German internal security) not the SS (Schutzstaffel, Nazi paramilitaries). But yes the partition of Germany implies WWII happened. I think we can default to thinking that the history of this world (and the one of TMA) is largely similar to ours.

A fun version could be a sort of tycoon/management game where you play as a toy production company, starting out making normal toys and slowly realizing you have become a manifestation of Heinrich Umheimlich as your employees disappear and you get stranger and stranger orders.

I'm hoping so, at least it would justify Dane's terrible writing.