I don't agree with your assessment. Intersectionality means that different forms of oppression (and different magnitudes/degrees to them) affect individuals' lives differently based on one's CUMULATIVE mixture of those various attributes.

Intersectionality isn't limited to race and class -- and, for that matter, it isn't limited to sex, gender, ableness, and religion, either. It's inclusive of all of those characteristics, but it SHOULD be viewed in a broader and more holistic manner.