I’ll bet everyone employed at Pine Gap felt that one. Uninhabited area indeed. Its only the largest NSA,CIA,NRO installation on earth. They ran most if not all of the “Desert Storm” communications through there. (Google Pine Gap photos)
This earthquake's epicentre was about 270 miles from Pine Gap. Reference is made to Alice Springs (which Pine Gap is near) simply because there's so little out there that a settlement hundreds of miles away is the only one people are likely to have heard of. The area where the quake was centered really is almost totally uninhabited. It's unlikely there was a single human being within 50 miles - Kaltukatjara is the nearest town about 60 miles away with a population of about 300.
People at Pine Gap could have felt it but it wouldn't have been all that strong at that point. When I talked about it being fortunate that the area is uninhabited, I'm talking about the radius in which significant damage could have occurred - and it's unlikely there was anything in that range.