Do primate RGCs have overlapping receptive fields?
Short answer
Associated ON- and OFF-center retinal ganglion cells can show 100% overlap in their receptive field.  

Background
When looking at the elementary neurophysiology of the retina, we can see that a single cone generally synapses onto two bipolars. Because photoreceptor cells hyperpolarize when illuminated, glutamate release from their synapse is inhibited. In turn, OFF-center bipolar cells are hyperpolarized and ON-center bipolars are depolarized. The OFF-center bipolar synapses onto an OFF-center retinal ganglion cell (RGC), while the ON-center synapses onto an ON-center RGC (Fig. 1).


 Retinal circuitry linking cones to bipolar cells (left panel) and bipolar cells to retinal ganglion cells (right panel). source: Washington University.

Then to your question - the basic circuitry shows that the ON- and OFF-center RGCs receive their input from a single cone and hence have 100% overlapping field. In the foveal region, bipolars link 1:1 on cones, as in Fig. 1, so in this example case, they show 100% overlap.

Note that there are an estimated 30 types of retinal ganglion cells, about half of them being not even described yet, as per a 2015 review article (Sanes &amp; Masland, 2015). Hence, this answer is anywhere from exhaustive, but it does show there can be substantial overlap between RGCs.  

Reference
- Sanes &amp; Masland, Ann Rev Neurosci (2015); 38: 221-46