The Shield of Zorek's Favor, Scorpion's Kiss and the Duskblade all three say that "this lieutenant [carrying the relic]" gains some abilty. Notably the Duskblade adds a surge ability to the carriers attack.
In contrast The Shadow Rune says that "Each of your attacks gain: […]". in combination with the rules book page 22 where it says that "[…] the relic's abilities can be used by the overlord" (and not "by the lieutenant carrying the relic") this can be constructed to mean that your attacks refers to any attacks the overlord makes (through his monsters).
This seems to me to make the rune really strong and I'd say that to be a miss-construction of the rules. But as I do not yet have a feel for the power level of items and relics in the game I'm interested in other opinions.