Any nuke set off in low Earth orbit, where all the military stuff is, presumably, would cook a few satellites in the nearby vicinity, but the rad belts are further out. Only LEO stuff with a high orbital inclination (i.e. passing through the auroral zone) would see prolonged exposure. We build military stuff with some pretty beefy rad shielding, I'm sure. Jupiter's natural radiation environment is pretty crazy too, we had to thicken up everything for JUNO. Dat magnetosphere. But yes, it does worry me that a detonation of an intercepted nuke or two in space could knock out enough military satellites to initiate a chain of events that would play out no better than if the first nuke or two had made it to their targets. I guess a lot of it depends on if the things go off or not. It would not surprise me to learn that the Russians build their nukes with something like a deadman's switch, where if anything went wrong, it was rigged to blow, whereas the Responsible Nuclear Arsenal would only detonate if it knew it'd reached its target.

The directed photon thing would require enough precision that I do question whether or not the Russians are capable of developing it properly. The speed of light would be non-negligible, you'd have to aim ahead of anything you're trying to hit. It's one thing to aim for a satellite you've been tracking for days, months, or years vs. an ICBM (or multiple) with about a 20 minute window to detect, track, and aim for. And actually, I think directed photon beams are our best chance to de-orbit space junk, which would require even more precise tracking and beam directivity 'cuz most of that shit is on the order of a millimeter. So I hope it's being developed for non-military applications (he said, knowing full well that it's already out there in military use by at least one country.

edit: now I'm thinking about an ICBM capable of little jittery movements in space to evade this scenario. You could course correct once you got back down into atmosphere thick enough to absorb most stuff up in the X-ray regime. You'd need some hella powerful impulse thrusters, though. Now that sounds like a fun project.