Is your definition of a botnet one that compromises a system without user intention? Is it because the user installed an application willingly?

Vectors of compromise don't necessarily change behavior, just risk level.

A botnet, to me, has nothing to do with vectors of compromise but in the way they work. In a botnet, you have a bunch of compromised machines communicating with a command and control system that allows the systems to be used for any task, in effect. In this case, it seems to be used solely for spamming; they might be able to push in new emails, but that's about it. That doesn't seem like a botnet to me.

I guess the application of this instance your more discriminating objectivity is correct. That said, having a user install a malicious app could certainly be the beginnings of a bot-net.

Right. It's a technical term used incorrectly. If a journalist called a few teens selling weed a "drug cartel" they'd be likewise expected to correct it. These are (apparently) just rogue apps.