They had the graveyard to themselves?

Without more context (such as a direct quote of the text), the only thing which can be said is that to have something to oneself means that you alone possess it, at least temporarily. It is usually used to refer to a place, so that would mean that no other people were there--they had the place to themselves, and themselves alone.

More context might help, though. It could have been an ironic remark. People generally don't go to graveyards, other than to visit the grave site of a loved one. Particularly, people don't go to graveyards at night (superstitious fears), and as it was dusk, night was approaching. However, without seeing the text, there's no way to know if it was an example of wry, ironic humor.

When I was at college there was a graveyard directly opposite, which served as a short cut into town. Some of my fellow students were wary of walking through there at night, and instead walked along the alleyway that ran alongside the cemetery. This was particularly ironic, as the graveyard was hallowed ground, and the alleyway contained a suicide's grave.

Sorry Izzythepush, I am replying to the whole thrad not just you. Forgive my imputence.

"People", are always in a graveyard, be they living or dead and at dusk, no further burials, would occur. "They had the graveyard to themselves."