TMZ obtained video of The Game unloading a punch on an opposing player during a pick-up basketball game -- but we're told the guy threatened to unload a gun in Game's ass before the fight.
Sources connected to Game tell us the rapper says the punchee started things by throwing an elbow at Game ... who responded by elbowing him right back. Then it got really heated -- Game claims the guy said don't make me go to my gym bag because ... "I got that thing."
The clear hint was the guy had a gun.
What happened next was a case of punch or be punched -- we're told Game is saying the guy raised his fist first, and that's when Game threw his Tyson-tatted right hand.
The video doesn't appear to back up Game's claim about the guy being first to make a fist.
Game denies making any death threats as the victim claimed to cops. Police are still investigating.