No, Esben and the Witch is not a goth band, because they play Shoegaze/Post-Rock, while goth music consists of Gothic Rock and its derived genres, like Deathrock, Darkwave, Ethereal Wave, and Coldwave.

However, they do have a significant goth influence and even have some goth songs in their repertoire, like "Sylvan" and "Chorea".

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Esben and the Witch are Dead Can Dance, Hada, and Lycia.