I don't deny that carrier could regain dominance, but not by airborne rail guns. Think WWI-WWII; planes didn't dominate supersede battleships by carrying 18-inch guns... Currently, this thing is room sized, it dissipates an extra-oridnary amount of heat, and it requires the kind of energy that only a large ship could provide-- sort of analogous to the 14 inch gun of the WWI era, if you will. Aircraft may find a way to beat this, but probably not by outgunning it, and it will probably take a bit of time for this to happen.
From the Navy Powerpoint, the naval gun will shoot a 10 kg projectile at 2.5 km/sec. The recoil on that sucker would be a bit much for an airframe
What they want is an indirect-fire capability where the projectile is fired up in a sub-orbital trajectory at mach 7.5, and comes down up to 200 miles away at mach 5, with a 5 minute flight time