Let $p$ be a prime. We characterize the oriented right-angled Artin pro-$p$ groups whose $\mathbb{F}_p$-cohomology algebra yields no essential $n$-fold Massey products for every $n>2$, in terms of the associated digraph. Moreover, we show that the $\mathbb{F}_p$-cohomology algebra of such oriented right-angled Artin pro-$p$ groups is isomorphic to the exterior Stanley-Reisner $\mathbb{F}_p$-algebra associated to the same digraph. This work also aims at providing a concrete and group-theoretic introduction to the study of Massey products in Galois cohomology for non-specialists, especially graduate students working in profinite group theory.