NYS has not usurped federal power to control the border. The opposite has occurred. The Feds usurp the right of NYS to issue driver's licenses at their own discretion. As has been pointed out, a person doesn't need a driver's license at all to gain expedited entry status, anyway. Nor is it just Cuomo but rather the legislature as well.
Of course it's built on a lie. It's the Trump admin way of punishing New Yorkers for their state issuing licenses to undocumented people. It means they can be covered by auto liability insurance, just for starters. It clarifies how cops deal with them in traffic situations, as well. It's part of coming to terms with that thing Trumpsters reject vehemently, reality itself. It's perfectly clear that the Feds will not be deporting 11M people anytime RSN so some other constructive ways of dealing with them must be found. Or we can lie about it, like the Trump admin, so as to use it as a perpetual wedge issue. I mean, some problems are best left unsolved for electoral propaganda purposes, right?