Yes, The Eden House is definitely a goth band because most of their albums belong to the Gothic Rock and Ethereal Wave genres, which are among the core subgenres of goth music. Albums like Smoke & Mirrors, Half Life, and Songs For The Broken Ones are examples of their goth sound.
Some of the other goth artists that are similar to them are Adoration, This Burning Effigy, and Strange Boutique.
The Eden House is located in United Kingdom, active in 2007 — present. You can find more information about The Eden House on their GothDB band page.