Also, this is one of those rare cases where English doesn't have enough synonyms, because there's no positively-connotated form of "possessive" in the language. The Merriam-Webster thesaurus lists "jealous, protective, domineering, suspicious, envious, controlling, demanding, overprotective"... You get the idea. One positive word in the list, and even that one's somewhat sideways of the meaning.
Somewhat sideways or no, though, "protective" and "overprotective" both show up for a reason: part of claiming something as "yours" is taking responsibility for defending it from harm. And that's part of why she's getting possessive here, because Kohatu is refusing to believe that Ling Qi cares enough to keep Zhengui safe. To which "how dare you, he is MINE (and therefore I will protect him)" is appropriate!