Can a proverb be a short dialogue?
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.
It's not a proverb. These are proverbs:
- Haste makes waste
- A stitch in time saves nine.
- Ignorance is bliss
- Mustn't cry over spilt milk.
- You can catch more flies with honey than you can with vinegar.
- You can lead a horse to water, but you can't make him drink.
- Those who live in glass houses shouldn't throw stones.
It's not quite a fable, either:
A fable is a succinct fictional story, in prose or verse, that features animals, mythical creatures, plants, inanimate objects or forces of nature which are anthropomorphized (given human qualities such as verbal communication), and that illustrates or leads to an interpretation of a moral lesson (a "moral"), which may at the end be added explicitly in a pithy maxim.
I argue that it doesn't qualify as fable because there's no narrative on the part of the wolves, just the grandmother supposing.
Personally, I find it a poor setup for a moral. They're both wolves. Try leaving two wolves together in the morning having fed only one and see how many wolves you have at the end of the day.
I wouldn't even call it parable or adage. An adage would be something like don't count your wolves before you've shone a light in the den.