TL;DR The glia-to-neuron ratio is not sufficient in order to distinguish humans from other primates or mammals.
The figures of the glia-to-neuron ratio (GNR) being 10:1 come from old studies that either used guesstimates for the number of cells in either category or used methods that have since been improved. The newest estimates range about a 1:1 ratio for the whole brain as reviewed in von Bartheld et al. 2016. These authors comment on the evolution of the GNR:
[Comparative studies have] shown that brain size does not scale universally
with neuron number, that different mammalian species
such as primates and rodents scale differently, that cell
numbers in cerebral cortex and cerebellum evolve in a
coordinated fashion, and that glia density and sizes
vary much less than neuronal density and sizes. The
GNR is highly conserved between structures and species,
pointing to an important and close regulation of
glia numbers (scaling) in response to, or regulated by,
neuron density and neuron sizes.
At least in the cortex, cell numbers and size are kept to a minimum, as they take valuable space from what really matters, dendrites and axons (Chklovskii et al. 2004).