I don’t see that as being similar to Stagger at all. It’s a grab linker and to me looks as though it’s manual timing.
Let’s take Horn Breaker for instance. It could just be me, but if I start a combo with Horn Breaker all I can connect with properly is a light afterwards. If Horn Breaker caused a Stagger (and it’s already a super telegraphed and easily Shadow-Counterable move) Thunder would have more ability to follow up with various moves or button strengths.
Not that I think Horn Breaker is the best move to get Stagger for, (though it’s definitely up there) because it could also be used for one of the strengths of Skyfall, his back-HK command normal, or even a new move entirely.
I’m not big into frame data or anything, but I honestly believe Thunder should receive something with the new mechanic. The only characters bigger and physically stronger than he is are Aganos, possibly Tusk and possibly Glacius (who is taller, but I have no real way to judge physical strength for him!). It would be incredibly stupid to give Stagger to smaller characters without giving it to the bigger guys who more readily fit the concept of the move, an unwithstandable smash to the face…