Okay, I've played through the original 12 home video games for the Magnavox Odyssey. There are different ways of classifying them, but I'm going to stick to the simplest: by Video Gameplay. Other than Tennis which begets PONG, these games really can't be considered to have established any genres by themselves. I could classify them into the genre's as we know them in 2005 (as I've more or less been doing) but if I were staring at them in 1972/73 having never seen another home video game but for these, I think I might classify them thus:
The PONG variants:
All involve manipulating Player Spot while attempting to deflect the Ball Spot.
Tennis, Table Tennis, Football(?) and Hockey
I use the term PONG because it is well known. I should note that these games predate PONG and indeed the Table Tennis game is thought to have inspired PONG.Football is a little more special. It's more of a Sports Sim that uses the PONG mechanics to determine the success or failure of a play and then refines that result with randomly drawn cards and penalty/bonuses for play prediction. I'm not sure how to classify it when considering the accessorized play, so I'll leave it where it is for now, unless someone has something to suggest.
The MANEUVER variants
All involve manipulating your Player Spot in two dimensions without the added goal of deflecting and then manipulating the Ball Spot.
Submarine does so while avoiding being hit by the Ball Spot so it is a little different. Since one wins by the achievement of the Submarine Commander's Objective, one could also argue that it is primarily an early shooter. They wouldn't be wrong.
Ski: Stay on a trail, or maneuver yourself back on to the trail blindly.
Submarine: Stay on a trail while avoiding being shot.
Haunted House: Maneuver your Spot blindly through a the maze-like "negative space" between items.
Cat and Mouse: Out-maneuver your opponent.
Simon Says: Out-maneuver your opponent.
Again, when considering the accessorized aspects of play, some of these titles might classify differently. Haunted House and Simon Says, for example, both use a card collecting system for score keeping, which adds more "feelie flavor" to the playing of the games. I could classify them as "games that use cards for score keeping". Whatever.
No Video GamePlay
Roulette and States qualify more as board/card games during which the video screen is used, (poorly), as a randomizing device. Either game could be played without the TV as long as a sufficient way of generating a random number is used.
Analogic:is hard to classify, but it might fit best under "Puzzle". While there is a slight dexterity aspect in the manipulation of the Ball Spot to maintain "contact", this is significantly secondary to choosing a number to which to move and planning well enough so that one doesn't lead themselves into a dead end. (Though, I don't think one should have to worry about a dead end. In my opinion, that's a design flaw.)
Of course, these categories are arbitrary and subjective. One could also classify them under Themes like Sports, Shooter, Edutainment, Adventure etc . . . , or even to the different degrees that they each use accessories. Your mileage may vary. These are just how I've chosen to sort them out. Other games released for the system in 1972 may or may not fall into these categories.
Running Score: Ultraman in the lead with 6, Odyssey trailing with 5.00