I've had a look for any relevant explanations of how this bridge slide differs from HS2's others, and there's nothing definitive. It is bigger, and it does have one big design difference, but the fundamental method is the same - Freyssinet's autoripage.
The one major difference is that Radlett and Coventry had vertical flank walls, and the embankment had to be backfilled up to that. Kenilworth has sloping walls, serving as a struts supporting the ends of the deck of the box. Backfilling under that is clearly a more difficult operation, depending on how much support that fill provides for the bridge (which is unclear, at least to me).
There is an HS2 CGI of something similar to the Kenilworth slide (here from Construction Management magazine), though it isn't exactly the same in its details. Assuming the five plates scattered around the crane on each side form the transition from bridge deck to intact roadway, that's what the cranes must be there to lift. Mind you, five plates looks to few to span the full width of the deck.
I also found
a "how to" video from Freyssinet about Coventry here, which illustrates the technique and in particular the hidden bits like the cables. Most of the text you read (e.g. HS2's used by most other publications) is a bit misleading in talking about the box being guided by a raft. The box (bridge and floor slab as a rigid unit) is built on a slab, with a sliding joint between them. Then the box is pushed off the end of the slab onto bare earth with a pool of bentonite lubricant on top. At the end of the slide the box is just off the end of the slab, and the jacking rafts are still on it.
Freysinnet's video of Radlett is also worth a look.
That's why my 50mph road on the way to Leamington was downgraded by HS2 to a 30mph as well!
