No, Bring Me the Horizon is not a goth band, because they play Metalcore/Alternative Metal/Rock, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Bring Me the Horizon are Fields Of The Nephilim, Rosetta Stone, and The Sisters of Mercy.