Foi a ideia de Bill Paxton.
Como foi dito para UPROXX do próprio Bill Paxton,
(ênfase minha)
I'm not great at improvising on the spot. The stuff I improvised was stuff that wasn't in the script, but it was stuff that I'd throw at Jim [Cameron] in a rehearsal. Jim is a — his mind's like a steel trap. He'd remember something I'd said when we were rehearsing at a scene we were shooting 2 months later. He'd say, 'You said something when we rehearsing to Sigourney. You said something about the express elevator to hell…put that in here.' That was kind of cool, that was kind of fun. 'Game over, man,' was really the background of the character.
I figured…[Hudson] was kind of the enlisted version of Gorman who was the officer, [played by] Bill Hope. He probably came up on video games and back in those days you always … I don't think they do it anymore because I don't play video games but it always at the end of your quarter, [it said] 'Game over.'…'Wow, has anybody ever used that, I wonder? Because it's good.' I had no idea it would catch on.