This is a really interesting topic that has fascinated me in the past.
One of the most interesting things I've found about Stargate is that some of them have 1985 Atari Corp copyrights on the back of the box. There was very little of anything at all coming out for Atari video game systems in 1985. Most all copyrights found on cartridge boxes jump from 1984 Atari, Inc. to 1986 Atari Corp. Stargate I believe is the only Atari cartridge game I own with a 1985 copyright printed on the back of the box. I believe Gremlins on Atari 5200 is another one.
You're right to think that's not true. The movie and game are a decade apart and unrelated. I remember after receiving Stargate via mail order directly from Atari in 1993, really enjoying the game - already then as a classic - and seeing that a movie called Stargate was coming out in Fall, 1994. I remember Stargate was in theaters at the same time as Star Trek: Generations. Stargate the game and Stargate the film and television franchise should not be conflated.
The real issue is why and when did Atari release Stargate as Defender II? The Atari 2600 game was originally released as Stargate, the same name as the arcade version of the game. Only later was the 2600 version released as Defender II, as was the NES version.
I've never located anything definitive as to why this happened, but there are lots of guesses and assumptions out there. Clearly it may be pertinent to legal issues pertaining to the usage of the "Stargate" and "Defender" trademarks - possibly "Stargate" had not been fully secured, or they were looking to bolster their claim to the "Defender" trademark. It may have also been a marketing decision - arcade gamers may have been familiar with Stargate, but far more people already knew Defender. It's possible marketing research showed that the game would sell better as Defender II than Stargate.
Stargate was listed on the Atari Mail Order Form as Defender II. In 1993 my memories of most 2600 games were vague, and I had nothing to go by (no internet) except for the Atari Catalogs that came with the E.T. and Asteroids cartridges I had found on clearance at Kay-Bee Toys earlier that year. I knew Defender and people remembered it pretty fondly - I thought it looked pretty archaic, but knowing it was a "classic" I wanted to give it a try and ordered Defender II from Atari. (You can see all of this on my hand-written list of games I was ordering shown below - I only knew of "Defender 2" and not Stargate.) I will say, when Stargate showed up and I gave it a play, I was really, really impressed at the time by what they were able to do with a 2600 game. Stargate looked and played lightyears beyond what the original Defender had been. I was really into the Atari 7800 at the time, and I thought 2600 Stargate / Defender II looked and played nearly as well as what I would have wanted to see from a 7800 version of Defender. I thought it was a really well done game, and I'm glad 2600 gamers were able to get something like that on their system. I thought it blew away everything from the Intellivision, 5200, and ColecoVision.
Atari 7800 6th Grade Strategy Guide.pdf