I think a cover song is a weak analogy because covers are not done by the same artist. This isn't like Sega giving us their own take on Fire Emblem. This is Nintendo, the original artist, doing a re-recording of the same song. It's more of a remix.
Movie remakes also pretty much never have the same script as the original. They're remakes really only in the sense that have the same title and the general plot is similar. Most videogame remakes are like a director's cut. Very few are as a different as a movie remake is. Metroid: Zero Mission would be a rare example of a remake where it really feels like a complete overhaul. Most videogame remakes just improve the graphics and add a few bonus missions or levels. It's like a movie with improved special effects and deleted scenes put back in.
But that's the thing, isn't it? The two best remake examples I can think of are Metroid: Zero Mission and the Resident Evil REmake on the GameCube. Both games were more than just graphical updates, but also incorporated new gameplay mechanics; new story elements; and often played (if not completely redrew) with the level layout and puzzles to make them more entertaining to new and old fans alike. When I played both games, they felt like
new games, not just the old ones with a new coat of paint. From what I saw and read of Shadow Dragon, it was an old game with a particularly jarring new coat of paint because Nintendo didn't change much else to update the experience for a more modern gaming era. I get the feeling we can expect the same of this game, and that's just not interesting to me. I'd rather replay one of the newer games with more inviting gameplay features.