How is the change in Gibb's free energy a condition for spontaneity for reactions not happening under constant pressure conditions?
Gibbs energy have an another equation which is:-


So according to this equation spontaneity of a reaction depends both on the enthalpy change as well as entropy change.
We all know that a system attains stability as the system's energy is lowered that is it has to release energy. If in a reaction energy is released enthalpy change is negative.
We also know that a reaction is favoured in the direction of increased chaos or a positive entropy change.

So from this we can see that Enthalpy change is negative and entropy change is positive for a spontaneous reaction to take place and the overall equation of 

becomes negative that is Gibbs free energy must always be negative for a spontaneous reaction.....Can be applied to any reactions.
Hope this helps.