That said, I can't help but think the following:
1) Before software, there were already products and services.
2) Software came along, and was used by people providing products and services. In a way, this was already PaSH, kind of, just more indirectly and it wasn't called that as the emphasis was on the products and services provided, and not the software.
3) Software began being provided by "application service providers" (ASPs), which sort of evolved into SaaS (software as a service). We even sort of commandeered the term "services" as an abstraction over software/business services as in "web services".
4) Now we are talking about "software", plus the old meaning of "service", where the two are fused into one.
It's a new word (but not really a new concept) for a somewhat more recent organizational form ("service based organizations").