No, Her Despair is not a goth band, because they play Gothic Metal/Hard 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 "Blaspheme With Me" and "In the Arms of a Sadist".

If you want to dive into the goth music scene, some of the bands that might appeal to you if you enjoy Her Despair are Fields Of The Nephilim, Opened Paradise, and Sweet Ermengarde.