I would say it's on-topic.
1) It seems to be set in an alternate world with anachronistic technology and elements of fantasy/magic mixed throughout.
The books seem to be set in an alternate, "timeless" world with stylistic similarities to both the 19th century and the 1930s, though with contemporary, and seemingly anachronistic scientific knowledge. For instance, in The Hostile Hospital, the Baudelaire children send a message via Morse code on a telegraph, yet in the general store they are in, there is fiber-optic cable for sale
2) The film adaptation is classified as a fantasy movie
3) Your question was generally accepted:
Reading order for books in A Series of Unfortunate Events universe
One of the issues with YA and children's novels is that the can be hard to pin down into a genre, as they're often just thrown into the category of "Young Adult" or "Children's", without going further. We see the same things with movies that get classified as "Family" and nothing else, when they're clearly also sci-fi/fantasy.
However, going back to our policy on works with sci-fi/fantasy elements, I would say this point is most relevant here:
If you're not sure it's SF but you think a good case can be made for it, it's on-topic.
You've seemed to have made a case, another user commented that they think it's fantasy and got a number of upvotes. I think the case is made.