In this episode, was Miri saying whatever the landing party was working on was butting in on things that were not their business? Or was she just demeaning their activities in general? The word sounds silly to my ear, and I wish I knew how it sounded to someone who knows the word well.
It's both: Miri was feeling scorned and jealous, so she bitterly accused Kirk of butting in on the kids' little society. It was a sour grapes moment; if she can't have Kirk, he's no good.
As to how it sounded, the word is demeaning when it's said to your face, but it can also be light and facetious. Obviously it's crafted to sound like a Polish surname, to be funny, and I can say from experience it was common parlance in the northeast among working class, ethnic-but-assimilated Americans. "Don't be a buttinsky" is harsh and cutting when you're just trying to help, but "He's always a buttinsky" could be mild and even affectionate.