I read and continue to interpret the definition as “discrimination of someone as a Jew for being of the quality Jewish” regardless of how Jewish they actually are.

The “Jews as Jews” to put the focus on the perceived identity in the eye of the discriminator.

To link back to your examples, people persecuted, murdered, by the Nazis and their allies for being perceived as Jews fits the definition as the motive for persecution was “Jews as Jews”, not for (pardon the stereotypes coming but examples of not Nazi enough viewpoints coming) “Jews as having curly hair” or “Jews as being Communists/traitors”, but the perceived Jewishness itself. Regardless of reality.