I don’t want to defend the company, but making it out that the definition of “service game” is as clear as 2+2=4 is just wrong. Neologisms like this tend to be very malleable. You seem to think that the exclusive definition for a live service game being that it connects to a server. But even the Wikipedia article (https://en.m.wikipedia.org/wiki/Games_as_a_service), a source that is written by the general public and as such should obviously reflect the most common definition in use, says games as a service are defined by their revenue stream, not by being connected to a server.
I think very often, you assume that your own definition of a word it’s so obvious that everyone should understand it the exact same way as you and that anyone who disagrees is not only wrong by trying to drive you insane. This game marketing guy is being sleazy by using the definition of a game as a service that best fits his needs at the moment, but that doesn’t mean he is trying to gaslight you.