@firefly,
My niece was determined to have selective mutism - and I also thought about that - but assumed she was this way with her close family as well from boom's description. My niece was like that in school and around people she did not know well, but not around close family members. Also, she could go to school and was involved - simply would not talk. Instead when asked a question, she would whisper the answer to a friend and the friend would answer in class.
My best friend also had a boy with selective mutism and it was similar.
This description sounds a bit different where the child is completely withdrawal not just not talking - although I would guess there is probably different stages of this.
On the positive side, both of these children I know, now are loud! Especially my niece. And my friend's son got in trouble in school for talking. So if it such, it can be overcome.