So far I couldn't find any decent pictures, only this Youtube clip. The mechanised part of the parade (starting at 27:00) consisted of the Tigr, the BTR-82A and the new MRL "Tornado-G" (from 30:20)!
I finally found this - small - picture of the Tornado that was shown in Vladikavkaz. It differs somewhat from the "real" 2B17M especially the forward part of the launch tubes. That plate in front looks like the one from the 2B17-1 upgrade that was reveiled in 2003. Normally it should have the small boxes that contain the fuze setting devices. They are also lacking on the vehicle that was paraded in Perm (my post #50500).
Well, as I wrote there are some differences with the "real" Tornado. And if you watch the Youtube clip you will notice that the speaker announces the vehicle as "RSZO Tornado".
I wish the Russians would stick to one upgrade instead of making things always so complicated. It's the same with the combat aircraft, T-72 etc. And now the Grads. And why on earth do they put the Tornados (or modernised Grads) on Ural 4320, while on the other hand they have the 2B26 on KamAZ-5350?