The spiritual stats are those which would be rolled for most "weird shit" abilities, such as sorcery, chi healing, spirit journeys, and so on.
Not all characters with a high Tao stat need be mystical, however. A baker can be one with the Tao as much as a sorceror. In the baker's case, he may have shticks which allow him to bake bread for special occasions to influence the outcomes of those who eat them. These shticks would be powered off of Tao substats. OK, fine, it's always mystical, but not necessarily blatant "weird shit".
Your Tao acts like a Karma stat, signalling your overall communion with the deeper workings of the world. Peasants and the like tend to have a Tao of 0. They are simply unconnected to the greater scheme of things, living in the world rather than being a working part of it.
Your Chi is a measure of your spiritual essence; something which attempts to corrupt your spirit may damage your chi, and if you are engaged in a ritual magical battle with a foe, you may be attacking each other's chi instead of hit points.
Some spiritual and magical effects will not affect people with zeroes in all their Tao stats (peasants are unlikely to ever *be* in a ritual magical battle), though such people should not expect immunity to things like fireballs. Also, characters with Yang and/or Yin well above or below their Chi can be especially vulnerable to mystical attacks due to their lack of balance.
Fortunate use: (No shticks are needed for this use.)
You may add your Yang dice to an offensive/active roll once a run, and you may add your Yin dice to a defensive/passive roll once a run. You may add your Chi dice to any roll once a run.