How do elemental damage buffs work with non-explicit skill runes?

Solution 1:

What platform are you playing on? On PC, I see elemental tags explicitly listed for skill runes, like this:

I can tell you from experience that the answer to your question is yes: these runes convert the skill's damage to the listed element and will be affected by +elemental damage.

"Show Advanced Tooltips" under Options -> Gameplay toggles the display of this extra information.

Solution 2:

As you noticed, these runes have Holy and Lighting damage type icons and in fact do these types of damage accordingly. So they benefit from % bonus to elemental damage.

You can check wiki for more detailed runes descriptions:

Shattered Shield: increases the blast radius to 12 yards and the cone length to 30 yards, and damage to 740% plus 335% of Block Chance.

One on One: damage type changes to Lightning, and primary target is also stunned for 1.5 seconds, while other affected enemies are knocked back up to 30 yards.