Levels 3 (Trip to Skynet) and 4 (Skynet) were most likely based on extended "Future War" scenes in the original script for Terminator 2: Judgment Day (1991). These would have shown the Resistance winning the war, and John Connor entering the Skynet complex, where he would send Kyle Reese back in time to 1984. These scenes were ultimately never filmed due to budget and pacing issues.
This was the first video game voiced by celebrity; Arnold Schwarzenegger, Robert Patrick, and Eddie Furlong all reprised their respective roles (The Terminator, T-1000, & John Connor) from the film for this arcade game.