The service they provide is on-premises deployment, I guess. But what they are deploying is a product.

The relevant (unanswered?) question for this thread is who's operating and managing that deployment, and to what extent provider (or subcontracted FDEs) is involved in integrations. I would be surprised to learn of deployment actually being independently operated. Sure the machinery can be considered a product but associated service- and support engagements are at least as relevant to take into account.