Just for safety: The baby's parents are of course there while the two are playing. Nevertheless, the sweet velvet paw takes its job very carefully and makes every effort to keep the baby happy.
The best way to see how this works is in minute 1:26, when the eyes of cat and baby meet and the toddler suddenly shines like a world champion. The YouTube video says that the little four-month-old Elliotte and her seven-year-old babysitter are best friends. You can see that too!