I notice that the circuit topology in post #1 is designated "series feedback" in literature, e.g. **broken link removed**
It often uses a source connected transmission line or series inductor. But as already said, parasitic elements can be sufficient to fulfill the oscillation condition.
I don't think that harping on about terms will bring you far. There are different feedback terminologies used in different application ranges, e.g. the more descriptive series/shunt terminology in analog circuit design. RF circuits are however dealing with ports and impedances or S-parameters. In this application range, "series feedback" apparently refers to a topology where in- and output signal of the feedback path are using the same port.
I notice that your initial post is asking "why it's called ...?" I believe, the more interesting question is "how does it oscillate?". If you understand why, you don't necessarily need to answer the first one unless you are writing a text book or preparing a lecture.
For me, negative impedance is the intuitive way to understand the circuit operation.