Assumption behind Gibbs energy and maximum work
The whole point of Gibbs free energy is to quantify a bound on possible non-expansion work at constant p and T. That non-expansion work is implicit as part of the term "dU" which in the reversible case can be written as 

$$dU = -pdV + TdS + dw_{\text{non-exp,rev}}$$

The $-pdV$ term is the expansion work if the process is carried out reversibly. You remove that contribution by adding a  $pdV$  term:

$$dU + pdV= -pdV + TdS + dw_{\text{non-exp,rev}} + pdV = TdS + dw_{\text{non-exp,rev}}$$

Finally if you subtract the entropy term you are left with the maximum possible non-expansion work (obtained when the process is performed in a reversible fashion): 

$$dU + pdV - TdS= dw_{\text{non-exp,rev}}$$