Most of warhead verification is actually verifying a given weapon IS a real weapon (without giving away its internal design, which is the hard part), not that something is not a weapon because generally you're trying to keep an account of how many/where warheads are. Verifying a given missile isn't nuclear tipped is largely a non-issue at least in the current arms control regimes.

This method has no real way to identify materials, which is what you really need for warhead verification. It would be easily fooled by replacing a warhead with a dummy source, which is a big no-no because now there is a potential hole in the bookkeeping. Weapons grade material isn't actually that radioactive anyway; warheads aren't inert but measuring radiation from them is fairly challenging. Probably not hot enough to see easily with this laser approach, though I'm only speculating on that.

>Shame that a nuclear weapons treaty with limits and an inspections regime is more sci-fi than the technology needed to remotely verify the presence of a warhead

Well articulated. The early history of atomic weapons regulation hinges on precisely the difficulty of independent verification means (as well as judgements on whether or not an adversary would let you into their country without whack-a-mole style circumvention). I still think that verification technology is the main stumbling block. Neutrino detection is what I (and I bet ongoing orograms in the DoE) focus on for this purpose. We need to be able to figure out how to sense neutrinos order of magnitude more effectively than we can currently. Right now it feels like panning for gold silt with sieves as sparse as chicken-wire.