Is Gibbs free energy the sole determiner for spontaneity?
For a spontaneous process at constant temperature and pressure, $\Delta G$ must (emphasis on must) be negative. 

Spontaneity of a process , explicitly, depends on the enthalpy change and the entropy change. The Gibbs free energy change includes both these factors to predict the spontaneity of a process.

So, yes it can be said that Gibbs free energy change is the main factor that decides the spontaneity of a process.

Putting into better words, $\Delta G$ being negative is a consequence of a process being spontaneous.