Lots of ink has been spilled trying to describe what The Gun Club actually did. My take would be punked-up blues with a decidedly dark bent, though the overt blues influences seemed to dwindle a bit as the years passed.
Sex Beat - the opener on the album and The Gun Club song your grandma and other non-fans are probably most likely to have heard - owes a great deal to punk and not so much to blues. The stop and go bits provide a bit of drama and the lyrics, well...they're lyrics. Overall I find that the appeal of this one has waned some as the years have passed, while songs on the album that I used to skip over have become much more appealing.