That is not the Gibbs Free Energy at constant pressure and temperature.
Alphabetic soup definitions:
- $G$ - Gibbs free energy
- $H$ - enthalpy
- $T$ - temperature
- $S$ - entropy
- $P$ - pressure
- $V$ - volume
- $w$ - work
- $q$ - heat
- $U$ - internal energy
Definition of $G$ is $$G = H - TS$$
Definition of $H$ is $$H = U + PV$$
The total differential of $G$ is
$$dG = dU + PdV + VdP - TdS - SdT$$
The definition for the change in $U$ is $$dU = dq + dw$$
There are two kinds of work: pressure-volume work (pv) and non-pressure-volume work (non-pv)
$$dw = dw_{\mathrm{pv}} + dw_\mathrm{non-pv}$$
Thus, substituting we get
$$dG = dq - PdV + dw_\mathrm{non-pv} + PdV + VdP - TdS - SdT$$
If the process is (approximately) reversible:
$$T =\dfrac{dq}{dS}$$
Substituting $q = TdS$ and simplifying, we get:
$$dG = VdP - SdT + dw_\mathrm{non-pv}$$
At constant pressure, $dP=0$, and at constant temperature $dT = 0$.
Therefore:
$$dG = dw_\mathrm{non-pv}$$
Hence, Gibbs free energy is sort of a measure of useful work we can get out of a system.
$$w_\mathrm{non-pv\ by\ system} = - w_\mathrm{non-pv\ on\ system}$$