GIMMS NDVI3g grid cells not entirely square-shaped?
Your understanding is inaccurate. The shifts by $\frac{1^\circ}{24}$ are only relevant for figuring out, where the pixel centers are located and where to start when you are looking to find the right grid index for a certain point. As for the resolution, it is much simpler. We have $4320$ pixels covering $360^\circ$ in longitude direction, i.e. a resolution of $\frac{1^\circ}{12}$ and similarly for the latitudinal resolution.

As for the square-nature of these pixels, they are only squares in lat-lon coordinates, not in terms of length on the ground.