This doesn't sound at all like a "botnet" to me. Rather, it just sounds like people installed an application that uses the email facilities to send spam.

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.

Could this be actually desktop software masking as android software? I.e. communicate with Yahoo servers as would android app communicate and avoid may be some spam filters this way?

This didn't happen through apps installed from the Play Store, but from pirated apps, and apps taken from Chinese app stores.