A human activity involving physical exertion and skill as the primary focus of the activity, with elements of competition where rules and patterns of behaviour governing the activity exist formally through organisations and is generally recognised as a sport.

The simple answer is that in the United States, we use the noun “sport” to talk about any contest or game that involves physical activity. When we talk about “sports” we mean the plural form of the noun. That is how we talk about basketball, football and baseball as a group.