I don´t see why curling wouldn´t be considered a sport
"A sport is commonly defined as an organized, competitive, and skillful physical activity requiring commitment and fair play. It is governed by a set of rules or customs. In a sport the key factors are the physical capabilities and skills of the competitor when determining the outcome (winning or losing). The physical activity involves the movement of people, animals and/or a variety of objects such as balls and machines. In contrast, games such as card games and board games, though these could be called mind sports, require only mental skills. Non-competitive activities such as jogging and rock-climbing, are usually classified as recreations."
I think curling indeed demands "skillful physical activity" and it´s easy to see why chess for example, isn´t considered a sport.