M06-DFT computations have been applied to understand four catalytic systems which involved [Ru(Cp)(MeCN)3]PF6 or [Ru(Tp)(PPh3)(MeCN)2]PF6 as mediator and ortho-alkenylarylacetylene, terminal alkyne, and methanol as reactants. Potentially, the products of these systems could be dihydrobiphenylenes, 1,3-dienyl ether, and naphthalene. Remarkably, each system afforded product selectively. Our computed mechanisms successfully account for the chemo- and regioselectivities of these systems. Furthermore, the study demonstrates that the chameleon-like mono(carbene) intermediates formed via the intermolecular alkyne-alkyne oxidative coupling play a crucial role to complete the reactions. According to their geometric and electronic structures, three resonance structures were introduced to characterize their reactivity properties, which address the features of the classical alkyne-alkyne oxidative coupling intermediates, mono(carbene) species, and electrophilicity of the intermediates, respectively. The reactivity properties lead to three channels isomerizing the intermediates to three isomers. Surprisingly, the bis(carbene) isomers, which are similar to the bis(carbene) intermediates generally considered to be crucial in the neutral RuCpCl-catalyzed systems, are accessible but not reactive enough to continue the subsequent reaction steps partially due to aromaticity. The other two isomers continue subsequent reaction steps. These findings may help not only to understand the four specific catalytic reactions but also to advance the [2 + 2 + 2] synthetic methodology.