No -- the "international surcharge" does earn PQPs. It's simply being categorized differently by the third-party booking site than it is by United.com. Technically, it's not part of the fare -- it's a separate fee (hence the use of the word surcharge). However, this type of fee does generate PQPs.

That's not to say that there might not be some other provision of this fare that makes it earn differently; it could be a bulk fare, for example, or explicitly state that it's non-mileage-earning. But you're interpreting the cost breakdown incorrectly; there's nothing in that which would limit your PQPs.