So I looked it up and yes, there is a term for this: instead of Deus Ex Machina, it's called Diabulus Ex Machina. "The introduction of an unexpected new event, character, ability, or object designed to ensure that things suddenly get much worse for the protagonists", not real thought put behind it, just for the sake of introducing conflict.
It becomes even funnier when you consider that yes, if he kills him, then 3 girls end as collateral, but by following his instruction, that gets bumped to 4. Masterful gambit Uruma. And also, let me guess, the "game" has to do with them getting raped. Surely it would be a first and a radical new idea for the author huh?