The new version benefits from 29 years of technological advancement by, among other things, displaying the player avatar as a person instead of simply disembodied cartoon eyes. The gameplay still involves avoiding ghosts and looking for pieces of a broken urn, but now also includes puzzles, bosses, and what sounds like a much larger environment than the original house, with "towers, basements and catacombs."
The new Haunted House will be out in September, and you can see a spooky trailer after the break. Now that Atari's started remaking its old games again, what's next? Circus Atari for Kinect? It would make more sense than that other Kinect circus thing.
[Update: Shacknews confirmed with Atari that Haunted House will be a retail Wii game -- not WiiWare.]