Haunted House! The thumbnail on the bottom is a shot of the same overlay with all of the transparent stuff cut out.
EDIT: I forgot to say why I thought this qualified as the first home adventure game. Your mileage may vary. Unlike the other games that came with the Odyssey console, Haunted House has many traits of an "adventure" genre game in a prototypical state. It gives the player a tangible setting through which to wander; items to find and "pick up"; and a role to play, that of the Detective. Of course, what is missing is any kind of puzzle element which, one could argue, is essential to the adventure genre. Okay, so it's a stretch. I'm just saying it's more like an adventure game than any other game on this console. (if I can call Submarine a "shooter", then I'm calling this an "adventure".) END EDIT
I love the Überlay for this game. It's a silhouette of a stereotypical haunted house. The house is three stories tall and filled with items such as bats, cats, skulls and candelabra. You play the game by moving your Detective through the house and "lighting" each item one at a time, in order, as specified by drawn cards. "Lighting" involves moving your TV square behind an item which causes it to glow. If you successfully light the item, you collect the item's card. Most of the house is opaque, so if your Player Spot isn't behind an item and isn't shining through a window (and it isn't supposed to be) you can't see it at all. The effect is like trying to sneak around a dark house in that you don't know when you are going to "bump" into something or suddenly shine your light through a window. If you accidentally light a window, you lose the previous card you collected. You can also lose cards if you light an item out of order. You try to get through the whole house, collecting as many cards as possible.
The other player is the Ghost. At the beginning of the game, the Ghost hides his square behind an item while the Detective is out of the room (literally, not looking at the TV). During the game, when the Detective gets one item away from the Ghost's hiding spot, the Ghost appears, saying "Boo!". The Detective must sneak by without touching the Ghost. If he does touch it, the Ghost disappears and takes half of the Detective's collected item cards with him.
At the top of the house is a secret message which allows the Detective to draw a card from the Secret Message deck. The message tells the Detective to go back and take a card he might have missed, or give back a card he might already have acquired. It's also a means of sending the Detective back to an earlier point in the house and giving them another chance to acquire a missed card.
After the first Detective's turn, the players swap roles. This game is actually for two or more players, so you could have as many Detective's and Ghosts as you can stand, all performing one after the other.
This is best described as a charming game. The art on the cards is cute. The Überlay, as I mention above, is cool. The gameplay, while not exactly engrossing, can be a good time, if you bring to it a good sense of play and humor.
My son and I enjoy it, meaning we've played it on more than one occasion, believe it or not. In my ratings scale, this was worth missing one episode of Ultraman.
The Score: Ultraman: 4, Odyssey: 3.0
Analogic is next which I think is the first example of a science fiction themed video game for the home.