Looking at art from a Gramscian perspective isn't interesting because of what it tells you about the art, it's interesting because of what looking at the art tells you about the ideology that produced it. Hamilton is the lens to look through, not the thing you're looking at. It's a fault of the essay that that wasn't clear, but the passage kleinbl00 quoted is the meat
In that respect, Hamilton probably is the “musical of the Obama era,” as The New Yorker called it. Contemporary progressivism has come to mean papering over material inequality with representational diversity. The president will continue to expand the national security state at the same rate as his predecessor, but at least he will be black. Predatory lending will drain the wealth from African American communities, but the board of Goldman Sachs will have several black members. Inequality will be rampant and worsening, but the 1% will at least “look like America.” The actual racial injustices of our time will continue unabated, but the power structure will be diversified so that nobody feels quite so bad about it. Hamilton is simply this tendency’s cultural-historical equivalent; instead of worrying ourselves about the brutal origins of the American state, and the lasting economic effects of those early inequities, we can simply turn the Founding Fathers black and enjoy the show.