I don't know about Storm Shadow, but I don't know how much they'd gain by reverse-engineering ATACMS. Russia's perfectly capable of building short-range ballistic missiles. I don't know whether they have any cluster ballistic missiles, but I don't imagine that there's anything that interesting there.

It's also an older weapon, and the US is replacing it with the PrSM.

I think they're engine units, yeah. "Booster" implies there's some sort of second stage, so that's not really the right word.

But yeah, these were NOT shot down, they're just the engine units that fall to the ground somewhere behind the target after delivering it's payload.

If these had been shot down, they'd look a lot more like the Stormshadow above, ripped to pieces (and probably with the warhead attached)

Edit: actually, a Stormshadow/Scalp in hard-target mode might also look like this, since most of the rear end would just kinda smack 'harmlessly' into the hard target after delivering the penetrator and follow-up separately.

The nose section isn't shown, which is what would be present on an intercepted missile.

You appear to be correct. I'll fix the title.