If we're going to do proof by paper (always dangerous in psychology, but never mind), consider this about IQ:
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4557354/
The evidence that IQ predicts success is dubious, and certainly not settled.
I also consider him wrong about EQ, although for more anecdotal reasons:
I have known people who can read individuals and social situations with extraordinary skill, make astonishingly accurate predictions about social and personal outcomes, and manipulate both with extraordinary efficiency and effectiveness.
I've also known high-IQ individuals who were worse than average at all of the above, and who suffered poor social, political, and financial outcomes as a result.
So IMO EQ is a recognisable skill, and it's clearly not the same as agreeableness in the Big Five.
It may not have been well-defined or well-researched in psychology, and the original book definition may not be accurate either. (I haven't read Golman, so I don't know what he says about it.)
But it's nonsense to pretend it simply doesn't exist.