Why baby animals seem "cute" to us? I understand why babies seem cute to us from an evolutionary point of view: They need our protection and love to grow, so it's beneficial for them to look good for us, or at least their parents, since that makes them more likely to be taken care of.

But why does this pattern repeat with baby animals? It seems that small puppies or kitten appear cute to a large number of people, so how does that make evolutionary sense? Do they remind us of our babies? Did domestic animals evolve to be "cute" in order for us to take care of them?
What you are referring to is broadly known as baby schema. However, does this not only apply to human babies, but actually to most mammals which need (parental)care. Certain features in the mammal trigger the release of hormones, which in turn will/can trigger caretaking behaviour in humans. The hormone release is associated with the eye and head shape. 
The reason behind this “phenomenon” is to provide and warrant for the safety and well-being of the baby (evolutionary benefit). Of course, this works also with the non-parents of the mammal, which provides that the animal baby’s well-being is also ensured if the parents are not available to do it. 
Also, the cuteness does not only apply to humans, but is very interspecific, hence the reason why we sometimes here about babies being raised by wolves, or orphan kitten being cared after by a dog.