The standard Gibbs energy change given allows us to calculate the equilibrium constant K through the equation ΔGo = - RT ln K. Given that ΔGo = - 2.90 kJ, K = 3.22 at 298 K. To predict the spontaneity of the reaction you need to know the value of ΔG under the given conditions. If ΔG is negative, then the reaction is spontaneous up to equilibrium. The two should not be mixed up, although it is a common mistake made.
Now, if you know the transition state theory in chemical kinetics, the rate of a reaction is controlled by its activation Gibbs energy ΔG#. If the value of ΔS# is zero or negligible, then activation energy controls the rate. It so happens that for the reaction given the activation energy is very large so that the reaction is extremely slow at 298 K, so slow that diamond doesn't appear at all to change to graphite.