The movie is set in a world where mankind has been at war with the mysterious lifeforms known as Image for over half a century. Renton joined the battleship Gekko-go as a member 8 years ago to search for the kidnapped Eureka. Now, in the battlefield, he will meet her again.
Dominic is supposed to be a teacher to Renton and Eureka when they lived in Warsaw 8 years ago. One day after telling them about the legend surrounding the Snow Moon Flowers, he vanishes. Eureka is described as a young girl whose body reacts strangely to direct sunlight. She's captured by the military and kept as their most guarded secret. To get her back, he entered the military. 8 years later, Renton will enter the battlefield with his favorite mech Nirvash.
The article goes on to specify that the story is brand new, and while the names and circumstances might be the same, the worldview and scenario is completely original. It also mentions that while there will be many new animated scenes in the movie, "by rearranging the scenes from the TV series footage, a brand new story and drama can be shown."
I don't have the issue of Newtype myself yet, since it'll only be out officially this weekend. When I do I'll put up nice scans for the article.
P.S. The cast listing in the article lists Renton, Eureka, Holland, Talho, Dominic and Anemone. So those are definitely in the movie at least.