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Just 4 days before Damontre Moore was cut by the Dallas Cowboys, the NFL defensive end was in a crazy street brawl in Texas ... and it sounds like someone fired a gun.

TMZ Sports obtained footage from the Oct. 20 incident outside of Bottled Blonde beer garden -- where 25-year-old Moore was getting into it with a group of guys.

One witness tells us the fight was over a woman -- but the details are unclear.

What we do know ... Moore tries to fight two guys -- and ends up getting jumped pretty bad. One guy puts Moore in a headlock while 2 other guys swing on him.

Eventually, Moore gets out -- and tries to jump through the sunroof of a Porsche to try and punch the fleeing attackers. As the car peels out, you can hear what sounds like a gunshot.

Cops were called to the scene at 2:10 AM for possible shots fired -- but everyone left, so no arrests were made.

Moore was a member of the Cowboys at the time of the incident -- but was cut 4 days later, reportedly for "football reasons" ... to make room for another player on the roster.