The notes seem to ignore the text, which says that Christ, although in the form of God,  emptied himself, not regarding equality with God as something to be prized. Which has caused theologians no end of worry. How could Christ empty himself? So they sought to find a missing genitive: what did he empty from himself? Your notes think it refers to  proper recognition, but the text says nothing of the sort, stating  simply he emptied "himself," being no longer in the form (essence) of God. That does not easily fit onto the later theology of divine essences. But there it is!