How Battlemage rune enchant mechanism works? (Lightning strike warden)

Hi,

I can't find a proper answer for this.
I purchased an imperial claw with added fire, cold and lightning dmg for my lightning strike warden build. there is a Battlemage rune enchant on it, which costs more than 5 divs.

since I'm still lacking the full understanding of how added elemental damage works (is it spell or melee dmg?), I'm not sure, if I get anything from this battlemage enchantment, since it adds to spell dmg. So I don't know, I can remove it, or which rune enchant could give more dps to the claw attack dmg.