I've had cats. The prey they brung me was never alive.
If you watch the video, this cat is also being very careful with each of the squirrel babies, pulling her lips over her teeth to carry it--the way cats do when they're carrying their own kittens.
Domestic animals are complex critters, is all I can say.
Cat caught and brought a chipmunk into a friends house then tired of playing with it. It took him a week to catch and remove the chipmunk.