I'd say the thing is more of a choke or a reactor than a transformer. A transformer in the most basic definition has a primary and a secondary winding, but the lil ballast has just one coil (at least for a single bulb deal).
A transformer connected in this way is essentially a choke, which, in this application, provides variable current limiting, which as we both know, is all a ballast does.
You're absolutely right though, the stupid thing looks just like a transformer, it's just connected into the circuit differently.
In the end, one could call a ballast a transformer, a transformer a choke, a choke a reactor, and a reactor a ballast and round and round and round and round...
In the end, when we are talking about magnetic ballasts, we're talking about a big coil of wire wrapped around a big iron core, so I'd agree with you, the stupid thing is just a transformer, and I'd certainly agree with you that it looks just like one.
As for the life... well, you get what you pay for, right? I've never seen one cost more than 10 bucks. Junk in, junk out.