Your observation about the root of the word might be accurate, but (in my personal view unfortunately) is not relevant. "Plagiarism" is now used to describe previously published (and in some cases unpublished!) work that is being "recycled", regardless of author, without explicitly noting it to be such.
I'm not defending the usage, I'm simply explaining how the term is now used. Language mutates, origins are lost, and usage evolves.
You may choose to quote dictionary definitions, but dictionaries document usage, and of necessity can never be fully up-to-date with more recent changes. This is especially true when the terms are being interpreted within a specific context. In many academic environments "self-plagiarism" is an adaptation of the original concept to indicate that students cannot repeatedly submit the same work over and over again. They will say something like "Work for this accreditation must be new and original" and then use the term "self-plagiarism" to describe when that stipulation is breached.
As I say, language evolves. People even say "The proof is in the pudding" and "I could care less". These are idioms that convey meaning as an entirety and are not to be interpreted according to the meaning of the words therein.
Similarly, now in some contexts "self-plagiarism" is a term used to describe recycling one's own work. Sometimes it's fine, sometimes it's not.
Love it, like it, or loathe it, the term exists and describes "A Thing(tm)".