It is indeed a sum type, but I don't think that is why (or true of all sum types, or less true of product types). It sounds like they are conflating "enum"?

As an example of a product type for whom we can define every possible representation: ((),()) has precisely one representation.

As an exampe of a sum type for whom there are infinite representations: (Either String Integer)

My understanding has it that it is called a sum type because 1) for finite types the number of representations is the sum of the number of representations under each tag, and 2) it behaves more generally like a sum (a^x * a^y = a^(x+y) is an equality in arithmetic, (x -> a, y -> a) is isomorphic to ((Either x y) -> a) in programming).