Young Adult (YA) literature is a greased pig, hard to catch and even harder to hold onto. Some define it broadly, pretty much including any work of fiction with an adolescent who is 13-19 years old. With a protagonist who is younger than that it's either MG or "Children's." With a slightly older protagonist, it's now popular to call it "New Adult" (a very hot genre, by the way). Some of the narrower definitions touch upon style (straightforward) and themes (coming of age, etc). There are several tropes in YA, which vary depending on the more specific genre classification. In other words, you can put YA in front of any standard genre and it's considered a new genre (YA Romance, YA Horror, YA Fantasy, etc.).
The problem lies in the practice. Although a true genre should have somewhat consistent themes and tropes, current practice is to classify just about anything with an adolescent protagonist as YA. So if it's a fantasy story with a young protagonist, it's YA Fantasy. If it's a romance with a young protagonist, it's YA Romance. The list goes on.
So then authors who did not write their books for young adults become labeled "YA authors." Mark Twain did not consider his Huckleberry Finn a YA novel, but how often is it marketed as such? Harper Lee didn't write To Kill a Mockingbird for children, but it has a young protagonist, so it's marketed YA or even MG. Shouldn't the author's intent have something to do with it? Additionally, both of these novels have found an adult audience, and that audience may even be embarrassed to admit their favorite book is a "Children's Book." Myself, I enjoyed A of GG a lot, but would be embarrassed to admit that in many circles because it's considered a children's book.
With these things in mind, yes, Anne of Green Gables is readily classified YA (or more accurately MG since young readers tend to read protagonists slightly older than themselves), but doing so could leave a large chunk of its potential audience on the table. Yes, the protagonist is an adolescent, and the story line could easily be classified a "coming of age" story, but there is more to it than that. How many YA readers will laugh knowingly at Anne's plights, vocabulary, and attitudes? How many of them will truly understand why Matthew and Marilla (or Aunt Josephine, for that matter) are drawn to Anne? Wouldn't many young readers be frustrated with Anne's decision to turn down the scholarship and stay with Marilla, and idea older readers might find comforting?
A of GG doesn't moralize like many of its predecessors, preaching the "right" way for children to behave, at least not in all aspects of the story. Earlier novels aimed at children might not dare make a heroine who is essentially rewarded for being stubborn and sassing her elders. If it were intended for YA audiences, that aspect of A of GG could be problematic. As Gammel points out, writing this story was a sort of self-help for Montgomery, a cathartic exorcism of her own demons.
All that said, calling this story YA depends on your definition (or practice) in classifying anything YA. By current practice, sure it's a YA predecessor of all those other YA books with young protagonists. But I would argue many of those other stories are misclassified as well.