Breathtaking list!-

There's also another tented outfit in the Sahara desert in Morocco with a name I can't remember off-hand.

Genghis Khan Polo has tents in Mongolia, which I'd been meaning to visit for the longest time. There's an ambitious housing/hotel project in Ordos, Inner Mongolia- am not sure what the updates are with that.

Sher Bagh in Ranthambore is an amazing property- there are kamaicha performances some nights, with music that Akbar the Great would have listened to during his campaign of Udaipur.

The hotels in Atacama are not in the desert proper but instead are located in the town of San Pedro. There's a desert hotel in Bolivia(truly in the middle of nowhere) but I would not classify that as luxury.