I'll not recount what is currently available elsewhere - see the helpful links to the google doc as well as the available autopsy on Dr. Hatterson. Instead I will simply post my early thoughts after reading the available information.
According to the NYMOAA, the stolen vase was dated back to approximately 1410 from China, but discovered in an Egyptian tomb presumed sealed some 200 years prior. According to the autopsy report for Dr. H, many of the internal organs, as well as the eyes, were removed from the body. No external injuries beyond the eyes and apparent gunshot wound were noted. The removal of the organs suggest a connection to the practices of Egyptian mummification.
I am currently unable to turn up any specific information on the vase, Emperor Tuan-Yo whos mark the vase bears, or the tomb of Queen Nefertari in which it was found. (Nevermind. I made the reference here.)
Also, what is behind the abrasions noted in the autopsy?
"However, minute punctate red abrasions are sparse on the skin up to 1/2 inch away from the wound edge. "
"There are red abrasions on the skin near the wound, but this does not appear consistent with stippling."
The autopsy is inconclusive on the origin of the abrasions.
My guess is that the abrasions were marks left from someone using a tool to extract the organs through the gunshot wound since no other marks were visible on the body according to the report. If ancient Egyptians could take out your brain through your nostrils perhaps they can take organs from a gunshot wound. If it isn't possible for a human because the wound is too small perhaps a Lovecraftian horror could. Speculation on Lovecraftian horrors are big at the moment.