Yes. More than that, it could also intercept Air-to-Air missiles...not just supersonic, but the upcoming next-generation hypersonic AA missiles.
If so, air wars are obsolete!
Uh, not quite. It is certainly a step forward. I would compare it's value to AWACs. It will seriously change the battlescape, and add an additional tool to the arsenal...that leverages all our others. But its still an early unproven prototype, and relatively "primitive" technology with limitations, i.e., the ability to stay airborne on station, within useful range, and operable...all of these factors perhaps impaired by weather...are all issues that need to weighed in every combat situation.
These lasers could theoretically be ship based, correct and could knock down antiship missiles?