What guarantees that there is a thermodynamic equilibrium in a closed chemical reaction network independently of the mass-action kinetics?
The equilibrium is determined by the thermodynamics, not by the kinetics.  The rate constants for the reaction kinetics must be consistent with the equilibrium determined by the thermodynamics.  For example, for a single reversible reaction, the reverse reaction rate constant must be equal to the forward rate constant divided by the equilibrium constant.