The game is being carefully constructed so that it doesn't contain big spoilers about the film: you can safely play and still enjoy the movie experience. "Spider-Man survives the movie" isn't exactly unexpected, after all.
Furthermore, making the game a follow-up to the film gives a lot more freedom to construct a story that works for a game, rather than trying to force a movie plot into a game shape.
Announcements are tied to marketing; this game's development has actually been quite long, especially for a movie tie-in. Beenox started working on it well before Spider-Man: Edge of Time was released.