So, Snape killed Dumbledore but he didn't cause his death. The curse and the potion did it. Nobody forced Dumbledore to put on the Ring neither to drink the potion. Dumbledore caused his own death and Snape just finished his life.

Did Snape really betray Dumbledore?

In return, Snape secretly allied himself with Dumbledore and the Order of the Phoenix as a double agent against Voldemort, using his powers of Occlumency to hide his betrayal from Voldemort. ... Even with his efforts to protect her, Snape felt responsible for Lily's death at Voldemort's hands.

Did Snape kill Dumbledore for Draco?

Instead, Snape killed Dumbledore, meaning that Malfoy could basically remain innocent. ... Malfoy fails to kill the wizard but is afraid that he's failed Voldemort. Instead, Snape acts as Malfoy's friend and instead kills Dumbledore, so Malfoy is off the hook.