Framing a woman as a prize that is to be competed for does do some heavy objectification in the movie. So, yeah, that.
Said women repeatedly calls out that behavior. The pointlessness and harm caused by macho culture is a theme throughout the movie.
If you think it's objectifying and sexist, that's a you problem.
Even as a child in 1960 I watched women fix aircraft, lifting out engines and stripping them.