I don't see how this was thought to be unique to humans? For instance, it seems to be common knowledge that big cats have to teach their kids to hunt by showing, for instance.

Edit: Going to the source papers clarifies a little, the hypothesis they're challenging relates specifically to social learning for "the knowledge of the production of a particular trait" and not learning in terms of recreating existing behaviors.

This would probably also be why pets and birds would be excluded. While they can learn and teach each other various things, most of those things are not relating to production and can be difficult to separate from behaviors that should be considered to already be part of the species' repertoire. Bird song or whale song may be a sort of learned "culture" but it's so endemic to their species that it's treated as distinct from what's being discussed.