I think some gothic stories can definitely be classified as horror. Perhaps not Jane Eyre or Wuthering Heights (though both contain horror elements), but certainly The Woman in Black, The Haunting of Hill House, The Turn of the Screw, or more recently, The Silent Companions. I've often thought The Hound of the Baskervilles feels more like gothic horror than crime thriller too.

Other gothic mysteries read more like romantic thrillers. Rebecca, for instance. My own published gothic mystery novels exist along this horror/thriller spectrum. The Birds Began to Sing is a gothic thriller (akin to something like Rebecca perhaps), Spectre of Springwell Forest is more a gothic horror (akin to something like The Woman in Black).

I'm an ardent horror fan and horror apologist, because I think there are horror stories that people are prejudiced against due to the disreputable nature of the horror label. I think many of these stories they'd actually find meaningful, cathartic, or just downright gripping, if they'd give them a chance. Just my two pennies worth.

I wrote more on the difference between horror and thriller suspense and how they blur here, if you're interested:

https://writingcooperative.com/thriller-suspense-vs-horror-suspense-e97c89270c64