No. I can't.
How could a "human mind" not be exclusively limited to humans?
My African Grey Parrot does not have a "human mind" he has a "parrot mind" because he's a parrot.
My mom's cat has a "cat mind" because she's a cat.
Whilst I agree that my parrot talks (or more specifically is capable of speech), and does demonstrate understanding of context, as in, he uses the word "toy" to describe his, well, toys. While he is capable of understanding context, I do not know, and probably will never know, if he conceptualizes his toys the same way I do. Maybe he thinks I'm a gigantic idiot because what I conceptualize as "a fun thing to play with" he sees as a "horrible invasion of his personal space" that he just can't seem to convince me to get rid of!
The Human Mind as you know it is not limited to humans because non-human creatures are capable of being virtually identical "people" without being actual Humans. A Neanderthal could be a person, an artificial "human" could be a person. So if Jimmy is playing an Elf, he can simulate that experience because the Elven race is "people" despite not being human. This is why. there's validity to playing other races and why they're not limited to being knockoff humans, because they have equal potential for character depth PLUS fun thinks like anatomical variance, lore, etc.
Your parrot example can be taken a little further though, because there is science behind the mind. If you scanned the parrot's brain and studied the chemicals inside, and compared it to your own, if they're the same then it means you think and feel the same. How we think and feel is informed by physical and chemical attributes with a lot of room for range.
In general, the way I'd recommend looking at it is that species differences, in regards to minds, are like subclasses under the "Mammal Mind" class, with Plant and whatever else as the other classes. Well, more like sub-sub-sub-sub-sub(...) classes, increasing in what stays the same, to the point that variation is so minor that it forms a gradient that no concrete borders can be drawn. We have too much measurably in common with other creatures for their minds to be alien to ours as you imply. I'm not saying you're the same as your cat, but I am saying that you and your cat do think and feel in a comparable manner. If you adjusted some sliders (more neurons here or there), your cat would have a ""human mind"" without being human. It would think and feel like you do, but from inside a cat body. But if a different creature naturally had that, then should a mind like that be categorized as "human," anyway? I say no, at least not once we share populations with non-human people.
This is proven to be the case because Earth has had non-human "Human Minds" in history, and discussing the hypotheticals of what will come in the future will inevitably bring up more cases of non-humans with what you call a "human mind". To return to a while back, I call that same thing "personhood" because what we feel is something that extends to others.
If you want to say the "Human mind is the human mind by definition," then we can go with that, but you'd still have to accept that a "Neanderthal Mind" or a "Dwarf Mind" are virtually the same thing, which is why I advocate for a different approach and use an umbrella term. If we assume comparable anatomy, the only difference between a Human Mind and a hypothetical Elven Mind are the little things like lifespan or dark vision, but the rest is the same. That's why it's easy and feasible to imagine being another creature, because you'd be you with superficial physical augmentations.
If any of this doesn't make sense, just ask me to clarify or something. I can't tell if this makes sense to you without that. I may go with one or two more replies but I've got new things I got to put attention towards so this can't go on forever.
