Stole this from wikipedia...https://en.wikipedia.org/wiki/Rooster_(song)
The song was written by Alice in Chains guitarist/vocalist Jerry Cantrell for his father, Jerry Cantrell Sr., who served with the U.S. Army during the Vietnam War. "Rooster" was a childhood nickname given to Cantrell Sr. by his great-grandfather, because of his perceived "cocky" attitude and his hair, which used to stick up on top of his head like a rooster's comb.
The "Rooster" nickname is often mistakenly attributed to a reference to men carrying the M60 machine gun ("Walking tall machine gun men"), the muzzle flash from which makes an outline or pattern reminiscent of a rooster's tail.[citation needed] It is also often mistakenly attributed to the 101st Airborne Division - in which Cantrell's father served[citation needed] - who wore shoulder sleeve insignia on their arms featuring a bald eagle. As there are no bald eagles in Vietnam, the closest thing to which the Vietnamese could draw a comparison was the chicken, thus leading to the pejorative "chicken men."[11]
Ultimately, the lyric you are pointing out is akin to the vietnamese coming to get the guy with the M60 Machine Gun or the "machine gun men." If you wanted to analogize that, you could say it's our competition coming to get us.