Being 'Gothic' or 'Goth' doesn't necessarily indicate any particular view on the existence of God, but is rather a sub-culture based primarily around music, fashion, art and literature.
The Origin of Goth
The Gothic subculture was a youth movement that originated around the post-punk music scene of 1980s Britain, and specifically at a nightclub known as 'The Batcave' located in Soho, central London. The original themes of Goth fused the outrageous fashion styling of punks with a spooky backdrop, and many of the concepts that we identify with 'Gothic culture' today actually originated from the bands that played the stage of the Batcave Club.
Do Goths Believe in God?
Whilst many rebellious youth and musical subcultures of the 1970s and 1980s (such as Punk, New Wave, New Romanticism) may have had a disdain for social structures such as politics and organized religion, there is nothing to suggest that they purposely set out to embrace or reject any particular theological or religious doctrine. Therefore, whilst it may be true that many young people involved in any counter-culture may view atheism (or the rejection of the existence of any deity) as the norm between themselves, it is by no means a requirement for being involved in any specific music or social scene.
Goths and Satanism
Over the decades, the idea of what Gothic culture represents has altered considerably from the early days of the Batcave Club. The emergence of several similar genres of music have blurred the lines a lot, and 'Goth' is now lazily used as a catch-all term to describe any form of alternative culture that is linked with the spooky and the macabre. The popular misconception that Goth music has anything to do with Satanism stems from this situation which causes lines between subcultures to be very difficult to distinguish.
To sum the situation up, the modern Goth scene is generally open to people of all creeds and beliefs (although snobbier Goths will insist that people at least dress the part). Whether Goths then choose to worship Satan, Santa, or Sandra Bullock is a completely separate and personal choice!