If the park is being operated by the central government, why would Americans call theirs a national park, instead of a federal park?
First off, this park is not in America; it's in Kenya. Second, saying it's a federal park sounds as though these parks are only available for people working in the government. In the United States, there are federal lands that are not necessarily open to the public due to special permits needed or laws that prohibit the public from accessing federal lands. These parks are not trying to showcase that the government is running them. These kinds of parks are meant to be enjoyed by everyone in the nation or showcase something special about the country. That's why we call them "national parks" instead of "federal parks."