It wouldn't. That's literally what coroutines are. In-process, lightweight, cooperative multitasking, built in as a language feature (or at least close enough to it).
It is not. Coroutines are a much more fundamental feature. They can be used to implement cooperative multitasking, and since that is such a common use case, they have gotten confused with the concept of cooperative multitasking.
Actual coroutines are a lot more flexible and interesting than just cooperative multitasking, though.
Coroutines and cooperative threading/multitasking are indeed threading. I assume they meant to say that it was neither preemptive nor parallel, which makes it somewhat limited. Some people think a system has to be one or both of those to be called threading.
For me, and for a vast majority of people I'd say, the word "threading" in common parlance implies pre-emptive scheduling with implicit synchronization points.
