You proved the author's point with your own rambling mess. You probably are a class first leftist if you think this essay is off-target. I think it is spot-on.
I would add, however, that class is more flexible than race, and that race is the more hardened and permanent form of oppression. I have been under the poverty level for part of my life and not, and both as a poor and not poor person, I am still discriminated against as a person of color.
I repeat: I have been able to climb out of poverty but NEVER out of my race/ethnicity, which is damaging regardless of poverty or not.