Yep, I got a decent video for a military. Hopefully there's a different vid for each victory type; the one I saw did look military-specific, lots of marching legions, fighting, etc.

My last couple of triumphs came from schwacking some rebel army stacks. So apparently stamping out a rebelled region counts, in addition to killing off a proper faction. The region in question was not originally my own; that might make a difference.