What makes the FAA think they have exclusive domain to define the word astronaut?

...the agency says would-be astronauts must have also "demonstrated activities during flight that were essential to public safety, or contributed to human space flight safety".

What exactly counts as such is determined by FAA officials.

This definition is selective and stupid. I agree a single, suborbital stunt flight doesn't make the cut in my personal vernacular. But if someone e.g. serves as a science officer on a flight or simply spends three months on the ISS doing nothing more than shooting professional photos I would call them an astronaut.

Christa McAuliffe didn't make it past launch but Wikipedia calls her an astronaut and I think you'd be hard-pressed to find anyone who wants to refute that.