This question is not directed at your example specifically: is there something beyond genetics that can make a species?
My reasoning is: I’ve seen animals lose some of their species’ behavior when separated from their parents too early (for puppies and kittens).
They end up missing behaviors and abilities that seem to be passed generationally rather than innate.
If this is the case, isn’t there something lost when a species is only kept alive domesticated or in zoos? Even if later reintroduced to the wild.
There are some examples in insects. They display courtship behavior at different moments in a day; this is good enough to make these two groups of flies/mosquitoes (I forget which one) do not mate with each other. If there are not more accidents, the mating will gradually become impossible in the future.
I'm not an expert on the subject (nor on philosophy), but I can't think of any examples of behaviour being relevant in species definition. Humans ourselves being a good example, that we are the same species regardless of which country/culture we're in, regardless of whether we have a disability that makes us non verbal, or... any other differences, really.