According to comments elsewhere, this may be another localization quirk causing confusion - the other languages apparently don't reference Rhalgr at all.
I think the idea behind the whole thing is that it's a manifestation of anger and vengeance, a nameless being stronger than even Bahamut...but the specific call out of Rhalgr in the English client muddies that interpretation.
Personally, I think that because the actual summoning didn't begin in earnest (afaik) until the moment Ilberd cast himself to his death that his desire had the strongest pull on what would be summoned, and he certainly didn't seem the type to be calling out to any version of Rhalgr, and that the deaths of the others served as a more general catalyst of aether - that some called out to a specific belief was less important than there being a surplus of aether generated by violent deaths.