To me, I thought that the Purity of Essence was more of mental thing. The Xel'Naga initially thought the Protoss were perfect as they were because of their Purity of Form, and with their communal link it appeared as if they had the Purity of Essence. It wasn't until the Protoss tribes started dividing and pursuing individual interests that the Xel'Naga realized that the Protoss fell short of having the Purity of Essence, and so they left in order to find the second piece of the puzzle, a race with the Essence the Protoss were lacking.
To add to that definition of the Purity of Essence, the Zerg did not fully achieve that until the Xel'Naga created the Overmind. With the Overmind, the Zerg became focused and of one mind. They were no longer individualistic, but acted and would even sacrifice themselves in order to further their race. That is what the Protoss had, but their pride showed that were truly lacking this oneness of mind.