No, Within Temptation is not a goth band, because they play Symphonic/Alternative/Gothic Metal, 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 Within Temptation are Mors Syphilitica, The Breath of Life, and The Dreamside.