I don't think they are completely wrong - "=>" is just implication. A hidden assumption in their diagrams is that circles of different colours are assumed to be different elements.
A morphism from orange to yellow means "O <= Y". From this, antisymmetry (and the hidden assumption) implies that "Y not <= O".
Totality is just the other way around (all two distinct elements are comparable in one direction).
A morphism from orange to yellow means "O <= Y". From this, antisymmetry (and the hidden assumption) implies that "Y not <= O".
Totality is just the other way around (all two distinct elements are comparable in one direction).