The description of this cat’s behavior is of a caring cat, Stewie, who wants to settle down the crying baby, Connar, with a gentle, paternal pat on the head. When Stewie first heard Connar he was confused and then he seems to have decided to step in to do his fatherly bit. The video maker writes: “Our cat Stewie helps put our new baby Connar to sleep”.
It could all be true and as stated but I doubt it. I don’t want to be killjoy but a realist. My guess is that like all domestic cats he likes to touch human companions. You often see cats reaching out with their paws to touch a person’s hand or the paw of another companion animal who is part of the family. In addition, cats like the scent of their human companions and Stewie is no different. Connar is his human “friend” and he wants to have contact with him. That is the extent of it.
Connar may have stopped crying because of Stewie’s touch. That is certainly possible. Alternatively, it may be coincidental. Cats do have emotions and connections with other animals. The domestic cat has, as we know, become quite social compared to his solitary wild ancestor. However, we have to be careful that we don’t ascribe human traits to domestic cats (anthropomorphise). It’s cute when we do but I am not sure it is a good idea.