Why is が added at the end of この小娘が? Is something being omitted here? Is it just a figure of speech?
Nothing is omitted there.
This 「が」 is a sentence-ending particle expressing insult, swearing, cussing, etc. It is often pronounced 「がっ」 by us native speakers, too.
"You little slip of a girl!" or
"You little bi***!"
The "right" translation will always depend on the context.
Lastly, the suffix of insult 「め」 is often inserted between the noun and the 「が（っ）」 (but not in that clip).
To be fair, it can be hard to say 「こむすめめ」 with the double-め when the last thing you want to do in cussing is to stutter.