The strange chant that Wai'Ki uttered was the Ancestral Tongue, a language of Old Spirits where every single word held power in them.
Even if Aldrich had a spell or passive that gave him Allspeak, the ability to understand every language, it still would not have let him understand this tongue for, according to the lore, it predated any regular spell.
In Elden World, the Elduin realm was ruled over by a variety of deities, but these gods were outsiders from other realms that had spread their influence upon the world.
Before them all, the Old Spirits ruled the land, acting as aspects of nature that represented everything from forests to the realm's three great moons.
With the arrival of the Elder Gods, however, the Old Spirits were cast away, their influence relegated only to the Soul Stream - the great spiritual realm where all souls were cast back into upon death, to be washed and cleansed anew for renewal and rebirth.