The three horizontal lines were first said to represent Heaven, Humanity, and the Earth by the philosopher Tung Chung-shu (who lived in the first century BCE). The vertical line is therefore the person of the king, or the institution of kingship, which unites the three.
Julia Ching of the University of Toronto wrote an essay entitled Son of Heaven: Sacral Kingship in Ancient China, which was published in 1997 in the journal T’oung Pao.
I have to admit that I haven’t read it in its entirety yet. However, I’d like to quote a few passages from the beginning of the paper, to give a general introduction to the topic of sacral kingship in China:
Whereas we find a differentiation of sacrifices depending on the persons—gods, spirits and ancestors—to whom they were offered, we do not have a term which is exactly parallel to the English word priest.
The Chou-li, or Institutes of Chou, actually begins, not with religious, but with civil officials engaged in central administration. Interestingly, one term used to designate the Chou chief minister (chung-tsai – 家宰 [jia zai – HC]) relates his office to grave mounds. And this office is also charged with ultimate supervision over the work of offering sacrifice, as well as over the ruler’s meals.
The division between the sacred and secular remains therefore blurred. Granted, of course, that the Institutes of Chou presents an idealised bureaucracy more than a real one. (p. 4-5)
One official in particular was specifically responsible for religious rites:
In ancient China, the official specifically charged with religious affairs was the minister of Rites (Ta-tsung po 大宗伯 [da zong bo – HC], literally Great Senior Lineage Official), who was always under royal supervision. In the Institutes of Chou, the king’s role is emphasised not only at the beginning of the book, but also just before the office of the minister of Rites is introduced.
Under royal supervision, this minister’s office was in charge of “the rituals toward heavenly deities, human ghosts, and earthly spirits, on which the state was founded, and for the sake of assisting the king in his task of building and protecting the country”.
Among other things, this man was in charge of sacrifices and sacrificial officials. He served the spirits and ghosts of the state with “rituals of good fortune”. He offered burnt sacrifices with smoke to the “Supreme Heaven and Lord-on-high”; he offered bullocks on firewood to [the spirits of] the sun, moon and stars.
In the absence of the ruler, he presided over the great sacrifices. In this capacity, he was associated with the king in the royal priestly duties. Presumably, in ancient times this man was a senior royal relative. (p. 5)
Ching goes on to discuss the differences between priests and magicians (and between prayers and invocations), whether or not there are “shamans” in Chinese culture (there certainly are spirit-mediums, so it depends on how much one draws a distinction between the two), the various titles translated as “king” and “emperor,” and various other topics.
If I have time, I may present further quotes from Ching’s essay in the future. Or, you can read the article in its entirety at the link provided above (which will require registration with the website, JSTOR, that has archived it).