I am wondering about the answer to the PSE question here: Electric Field inside a hollow ball, excentred of a homogeneous charged ball
I understand the solution, but I don't understand how it corresponds to the Gauss's law. The charge inside the hollow is equal to zero, so why isn't the electric field?
The superposition principle tells us that the field due to the two objects (a fully charged sphere, and a smaller sphere with opposite charge density) can be added together. It is entirely possible to have a non-zero electric field in a region without any charge in it (think for example about the space between the plates of a parallel plate capacitor). You just need a field whose divergence is zero, that is $\nabla \cdot E = 0$. This is true, for example, for a uniform field, or a field of the form $e\propto \frac{1}{r}$ .
The absence of a charge does not imply the absence of field - just the absence of divergence.
but I don't understand how it corresponds to the Gauss's law.
Gauss' law tells you that the electric flux through the surface that defines the hollow volume is zero since the charge enclosed is zero.
But that doesn't imply that the electric field is zero within the hollow volume only that the electric field is special in the sense that all of the field lines entering the volume leave the volume since there is no electric charge there on which electric field lines originate and/or terminate.
That is, as Floris points out, the electric field within the hollow volume has zero divergence.