Framing a woman as a prize that is to be competed for does do some heavy objectification in the movie. So, yeah, that.

That's a superficial reading.

Said women repeatedly calls out that behavior. The pointlessness and harm caused by macho culture is a theme throughout the movie.

The movie is pretty clear in its intent to show this as a bad thing. To the point of stating it out loud several times. The climactic fight ends with both men losing and nearly killing each other.

If you think it's objectifying and sexist, that's a you problem.

If that would be the only view of said woman, I'd wholeheartedly agree to this point. The movie (and generally life) is so much more and more complex, with good and bad sides which all belong on the screen to be watched and criticized.