Interaction between hexproof player + each opponent spells

[CptHaddock]

As an example my opponent has a Leyline of Sanctity out and I have a Deathrite Shaman out. This is just a standard game (e.g. 1v1). If I go to drain my opponent what happens? Does the removing of an instant or sorcery resolve and my opponent just not get drained 2 life or does the "each opponent" clause of DRS negate that?

Thanks in advance!

[Dice_Box]

Each opponent is not a targeted effect. That's why a Leyline stops the second two abilities of Liliana, but not the discard.

Short answer, if the card doesn't have the word "Target" on it, it's very likely not targeting anything/anyone.