While vampire lore originated in Christian countries, it has spread into non Christian countries. I have read some of the non Christian vampire fiction. There is one big difference between a Christian and a non Christian vampire. While a Christian vampire can be killed by the cross (or be scared away by the cross), the cross or holy water does not work on a Jewish vampire or a Hindu vampire. Other methods of killing (running water, sunlight etc.) are OK.
I remember reading a vampire story from India. The vampire was killed not by a cross, but by a trident.