Domino and Tile Games groups its three members by a single physical action: drawing or laying a small marked tile and matching it against what is already on the table. Almost nothing else connects them. Dominoes traces to two separate documented traditions with no established link between them: a Chinese tile set called pupai, recorded around 1120 AD in the Song dynasty, and a distinct Western double six domino tradition first documented in Italy in the eighteenth century. Whether the two traditions are related at all is debated among game historians rather than settled.
Mahjong reached its modern standardized form independently, in China's Jiangsu region in the second half of the nineteenth century, growing out of an older Chinese card game called madiao rather than out of the domino tradition. The popular story crediting Confucius with inventing mahjong is folklore, not documented history; the game reached Western players later still, mainly through simplified rule sets published in the 1920s by the American businessman Joseph Babcock.
Carcassonne breaks the pattern again. It was designed by Klaus-Jurgen Wrede and first published in Germany in 2000, winning the Spiel des Jahres award the following year. It shares the tile-laying mechanic with dominoes and mahjong but nothing else: no shared country, no shared century, and no documented lineage running back to either older game. The subcategory holds together because the physical move survived intact across roughly nine centuries and at least three unrelated inventions of it, not because the games themselves share a history.