Potential energy versus reaction coordinate (graph of Gibbs free energy) Does the potential energy scale in the above mentioned graph measure the Gibbs free energy of the system?

As the system always tries to achieve a minimum of free energy and chemical reactions are taking place can be considered a non-mechanical work (I'm not sure of it, as the system isn't in a state of chemical equilibrium if a reaction is taking place), potential energy should represent Gibbs free energy.

If not, how should I understand the potential energy of a reaction mixture?
There is a long explanation for that, however in short they are not the same thing. Free energy relates to thermodynamic systems with many particles and is governed by Boltzmann's distribution, a sum of all possible energy configurations, where F is the free energy of the system.

$Z = e^{- \frac{F}{kT}} = \sum_i e^{- \frac{E_i}{kT}}$

Potential energy is non-statistical and well-defined for one particle. Thermodynamic free energy (one type being Gibbs) is a subset of the total potential energy. Even though they may seem similar, they should not be confused and should not be interchanged.