I'm not quite following. According to the OP and the docs you linked, a subtype is defined by a base type and a predicate. In other words: You can view it as a subset of the set of elements of the base type. That's pretty much the standard definition of a subtype.

Object-oriented programming languages are not that different: The types induced by classes can easily be viewed as sets: A child class is a specialized version of its parent's class, hence a subtype/subset thereof if you define all the sets by declaring `instanceof` to be their predicate function.