If this is meant to be an explainer, that can't be simply implicit. The text actually seems full of imprecise claims, such as:

"All diagrams that look something different than the said chain diagram represent partial orders"

"The different linear orders that make up the partial order are called chains"

The Birkhoff theorem statement, which is materially wrong. A finite distributive lattice is not isomorphic to "the inclusion order of its join-irreducible elements".