No, an API is a contract. Just like an object or a class or a structure is not a DSL.
None of these modify the syntax or keywords of the language used to implement them, and only objects and classes actually have the ability to override operators.
Just grouping things together in a particular order and giving the group a name does not make a DSL.
Just grouping things together in a particular order and giving the group a name does not make a DSL.