The puzzle on the left is one of the two types of original domino that were marketed. It's a little fragile and is solved by placing the numbers in order with the other coloured version directly underneath. The puzzle on the right is a recent mass-produced version with coloured stickers. The stickered version is easier to work with, less fragile and the patterns are easier to spot with coloured stickers.
You tend to need more than your cube algorithms to solve a domino. There are also optimisations on cube algorithms that no longer need to preserve the middle layer of the cube.
The original domino is quite hard to get hold of. They don't seem to be produced like that any more. They command some fairly high prices in the second-hand market and are strictly a collector's piece. The modern dominoes go for around the same price as a standard cube and are available for sale online.