In other words, having a mind in this respect is being what Heidegger calls Dasein, and we might just call being a person. Neither is having the knowledge that you have abilities or social status. So whether or not someone or something has a mind is not determined from the first-person. You might have a mind without ever realizing it. All animals seem to have minds in the first sense.
Humans certainly have minds in both senses.
If so, they're mindful in both senses. If not, they're different from us in some important ways. This doesn't make them uninteresting, or unintelligent, or unworthy of ethical consideration. Neither of them are really, at least not in the way that, say, a grapefruit is a thing. And neither is the mind.