“What exactly is he getting at?”
He’s trying to claim that his detractors are not familiar with certain “markers” of the working class, but he’s doing it by reference to retail shopping, a female activity.
If they don’t know the difference between TJ Maxx and Kohl’s, it’s more likely because they are men, not because they are rich.
So even his attempt at working class cred is soy boyish.
If he had said “Home Depot and Harbor Freight”, he might have come off less prissy and prancy.