How could all of these genres describe a book thinner than a paperclip? Two reasons.
You'll find the tragedy and the historical fiction in Woolf's story of Shakespeare's sister. Woolf uses a real person from history (William Shakespeare) to weave a fictional story. And Judith Shakespeare ends up killing herself before she could use her considerable literary gift. So, a tragic historical fiction.
When Mary tells us all about how the writer's mind works—complete with the winding river (check out "Symbols"), she goes straight into philosophical literature. And check out the way she tops it off with her vision of the couple getting into the taxi cab (6.3). That is some real philosophical viewpoints there.
Okay, are you with us so far? We tend to associate parables with the New Testament, but a parable is just an allegory with a message, usually using humans instead. So—human figures? check. Short? check. Moral lesson? check and check. Woolf's message is that denying women opportunities, money, and privacy makes it impossible for them to write well, which is a huge loss for everyone.
Now that we've softened you up with a few easy ones, let's tackle the shaggy beast of Modernism.
Woolf is a major, major Modernist writer, and the thing about Modernism is that there are about as many ways of doing it as there are people writing it. Here, though, we can say that Woolf's Modernism involved thinking about thinking, then trying to get that down on paper as accurately as possible.
Right at the beginning Woolf tells us that she's "going to develop in your presence as fully and freely as I can the train of thought which led me to think [that women need money and rooms of their own in order to write fiction]" (1.1). That business about developing a thought "fully and freely" is something Modernists try to do. In other books like To the Lighthouse, Woolf uses fancy literary techniques to get us to really experience another person's thought.
A Room of One's Own isn't experimental in that way, but it sure does want us to feel what Mary's feeling.