The misogyny arises from the implied assumption that the woman is just the object of men's desire, that she has no will of her own or ability to act, except to comply with the wishes of whichever man reaches her. The story doesn't actually say any of that, but it is pretty strongly implied. There's also the implication that the physicist and engineer are male, but that's the lesser issue.
It's interesting to note that merely reversing the gender roles in the story causes the perceived problem to disappear, but doesn't address the real issue. This is because it's not the story itself that implies the misogyny, but the cultural subtext, and since that subtext assumes that men are actors and initiators that the man has decided to go along with the game. You can truly eliminate the problem by modifying the story to make the woman the organizer of the little game, which puts all three on equal footing. She's acting by setting the scenario up, the men are acting by deciding whether or not they wish to participate and if so, how.
The difference is subtle, but such subtle, unconscious biases in many different areas can and do often combine into significant -- though often completely unintentional -- bias against women.
As an aside, when we speak of the "objectification" of women, the original use of that word in that context means not object as in "thing", but object as in "direct object", from grammatical structure. The objectified person is one who is always acted upon rather than acting upon others. This story clearly indicates both meanings of the word: The woman in the story is an object of desire, in this case sexual. That's actually perfectly fine. Men and women both can be objects of sexual desire, and as long as the desire doesn't translate into unwelcome advances or into other negative effects, everyone appreciates being thought desirable. But the woman is also and object upon which the physicist or engineer will get to enact their will, and her will isn't relevant. That is the way in which objectification is negative.
Revising the story to make the woman the initiator of the game, while not removing the ability of the physicist and engineer to choose, makes all of the participants actors and none of them pure objects.