Well, first of all, the cartoon was on the air for over a year before the NES game was released. The miniseries ran in Dec. 1987 and the daily syndicated show started in Oct. 1988. The NES game didn't hit until May 1989.
That's all irrelevant though. While I don't dispute that the movie is decent kids fare, there's really no way you could argue that it was based on the game. I would be willing to accept an argument that the movie was based on the cartoon, even though the comics came first, simply because the cartoon had a far wider cultural impact than the comics did, but saying that the movie was in any way based upon the game is simply reaching too far.