Kittens & puppies are reassured when they play with you. Whenever I've brought a new kitten or puppy into the house, I lay right down on the floor with them, so I'm not this towering Godzilla monster staring down at them.
Then I encourage them to gently play with me, to nibble and bite a little, like that video, second above (not the psycho caged cat). They're "programmed" to want to play anyway, and it helps to alleviate the stress & fear they have from being in a strange place. I assume they figure that if they can gnaw on my finger, and I don't gobble them up in return, then they're in a safe environment.
And sometimes I sleep on the floor with them the first few nights, curled up in a blanket together, with an absorbent hospital bed pad under them, especially for a puppy. That initial bonding is crucial.