Overextension is normal
Overextension and related phenomena (including the opposite, underextension) are very common, even expected phases in language acquisition.
Some children call all four-legged animals "dogs" for a period, while others reject the idea that a chihuahua and a German Shepherd are both "dogs".
As a child, I thought that "park" meant only playground equipment. I guess my parents would ask, "Do you want to go to the park?" and I'd think of the only part that was interesting to me at that age.
Addition: (This is also what's happening in this famous clip... the girl is not clueless, but overextending!)
Your niece has a mental concept of what a kitty is, and she's doing the right thing by testing it out on new specimens, even if she has to refine her guesses later.
Directly correcting language errors is hit-or-miss, but it can't hurt
Correction of these usages by parents is not always effective.* All children have to figure out the boundaries of word meanings for themselves. This happens through trial and exposure.
But if you're concerned about ensuring she gets the right information and don't know how to explain the subtleties of animal taxonomy to a toddler... one way can be to gently prod her to think about it. Confirm part of her hypothesis, but add to it or problematize it:
— Yook, a kitty!
— Yes, look at the lion! Isn't he fierce?
The child becomes helpfully perplexed about the meaning of your comment and accommodates the new information, either now or later on when she observes that those around her don't say "kitty" when they see that animal. When you say "yes" but use a different word, she's likely to come to the right conclusion: that what she said isn't wrong but it isn't the best or most specific term.
Alternatively, there's no harm in directly correcting her. The worst that can happen is that she might ignore or contradict you (for now), and hey, if she's got some metalinguistic gifts she might actually listen and apply what you tell her directly.
— Yook, a kitty!
— That's not a kitty, honey — kitties live in our houses. It's a lion. Isn't he fierce?
To put it shortly, don't fret over it. Correct her directly or indirectly, or just let it slide. She will work it out, along with her other inevitable grammar mistakes, as she grows up.
* Indeed, children rarely learn from direct correction. Some types of errors, such as the one in the following exchange between a linguist and his son, are even harder to address through explicit instruction:
— Child: Want other one spoon, Daddy.
— Father: You mean, you want the other spoon.
— Child: Yes, I want other one spoon, please, Daddy.
— Father: Can you say "the other spoon"?
— Child: Other... one... spoon.
— Father: Say "other".
— Child: Other.
— Father: "Spoon."
— Child: Spoon.
— Father: "Other... spoon."
— Child: Other... spoon. Now give me other one spoon?