You are correct that a high degree of vertical integration does not necessitate market dominance.
I would like to add some nuance though: As the supply chain becomes longer, the value of vertical integration rises. Now if we acknowledge that bigger players can profit more from vertical integration as well, and assume that players play equally well, we have a "devil poops on the big pile" situation, pulling the market towards a monopoly as the bigger player gets to profit more.
So it's not got exactly ZERO to do with market dominance ;)
I would like to add some nuance though: As the supply chain becomes longer, the value of vertical integration rises. Now if we acknowledge that bigger players can profit more from vertical integration as well, and assume that players play equally well, we have a "devil poops on the big pile" situation, pulling the market towards a monopoly as the bigger player gets to profit more.
So it's not got exactly ZERO to do with market dominance ;)