The alternative would be a parable, but this feels a little short for that.
Having it formatted in this way with the name of the speaker indicated as in a play or script is part of what makes it seem strange, I expect.
I think, as a proverb, it seems more familiar if the conversation is abstracted: "The wise woman says to the child that there are two wolves in her heart, one loving and one vicious. When the child asks which will be the victor, she says it will be the one she feeds." But even this is longer than the typical proverb.
As a parable, I would expect it to be a somewhat more fleshed out narrative in which she and the child reason back and forth before she finally tells in the answer.
I would probably settle on parable, or if I felt uncomfortable with that designation, refer to it instead as "traditional short story about a Native American woman and her grandson," as you've done here.