Godai is a concept from Tendai sect Buddhism.
Rokkudai is a concept from Shingon sect Buddhism.
Actually, they aren't divided precisely among sects. There are fourfold, fivefold and sixfold models used depending on the context, sometimes expressed in nested series. The fivefold model is common as it mirrors the scheme of worldly buddhas emanating from Dainichi.
Japanese martial arts were influenced by the religious influences around them the same way that martial arts in other cultures were influenced by the religions around them. The quote you are refering to was drawing on Buddhist concepts, not necessarily concepts that are organic to the Bujinkan. As far as I know, there is no "godai" concept organic to the ryu ha in the Bujinkan.
It was, I believe, in relationship to Juppo Sessho.