If you look carefully at this video you will see that the cat has its ears lowered, a sign of fear. Its back is humped not relaxed. And it turns its head away from the human videoing it - another sign of fear. It also blinks rapidly.
Feigned sleep is found in rescue catteries and among wild animals in zoos. Humans do not recognise it. It is a sign of chronic stress and unhappiness.
This cat needs help. It needs a box to hide in and if it has one it will be more likely to come out and look around, knowing that it can retreat if need be. No rescue cat should be without a privacy area.
If a privacy area doesn't help enough, then it needs fostering in a home.
Stand up for rescue cats. Pass this information on.