No. Goth is generally its own thing.
Though, death metal can be gothy! Goth death metal does exist in the form of bands like Paradise Lost and Akercocke, whose music revels in sadness and old-school indulgence. Meanwhile, death doom, a merging of – you guessed it – death and doom metal, has a certain yearning and sorrow that goth music embodies. But goth, like black metal, is steeped in dramatic emotion, and often lies separate from death metal.
We assume this question is not really about goth, but goths, and is basically asking if your kid who wears all-black and spiked bracelets is a goth or a death metal fan. The answer is, maybe both? People can like two things.