It's common phrasing for somebody being made fun of. I assume that since the correspondence dinner has recently been a sort of roast of the administration by the press that she was using it in the "being targeted by jokes" sense, but who fucking knows anymore.

"Shots fired" is a very common idiom used to describe biting remarks in a speech aimed at a specific individual or group. It isn't unusual language at all.

https://en.wiktionary.org/wiki/shots_fired!