The introduction is significant, it sets the tone. The sharp angles and the march, characterized by stomps and punches, are very aggressive, very masculine. The music starts after about 2 minutes with the men now barely dressed. During the first verse we learn that Gaga is shy ("got both hands in her pocket", "hides true love en su bolsillo"), but not sexually. Once she chooses, she goes into the relation with abandon ("Nothing to lose"). As she sings notice the identical haircuts the men wear: phallic symbolism. The men are engaged in competition, Gaga hasn't yet joined the "dance."
The chorus then reveals that she's only willing to be intimate sexually; after the act she just wants her cigarette, doesn't want her name called, doesn't want a kiss. That would be too close.
During the second verse the imagery becomes more sexual. She's actively engaged with all the men, one at a time, a different bed for each. The lyrics acknowledge her old flames, the new flame has to "firefight, gotta cool the bad"
The sexual choreography continues into the start of the third chorus. When the chorus repeats we see Gaga robed, wearing multiple crosses. This is the first time we see all the men touching her simultaneously. She swallows the rosary, and the men lift her up in exaltation.
What happens next is significant. The men are now capped and dressed conservatively. The phallic symbolism and the masculine sexuality are gone. Their march is no longer aggressive. Gaga then appears wearing a machine gun bra. She is no longer a slave to her sexuality. She is empowered by it. She wields it. At the end of the video Gaga has her way with the men. There's no more competition, the sex is no longer violent. It's no coincidence she has the robe on as this happens. She embraced the Sacred Feminine.
The bigger picture is revealed in the background on the movie screen. War footage shows fire, violence, chaos. It shows a world in disarray, the result of a society too focused on the suppression of women through various means, the most significant of which is the shaming of women for having sex.