The Kemper has tons of gain available if the goal is to boost gain or the ability to place a parametric EQ before the amp if the goal is to shape the tonal response which allows far grater control than a TS would allow. Honestly, the this clip sounds as I would expect, a bit more "aggressive" than the real deal but not night and day IMHO...
You're just not fully understanding what the use of the TS infront of a high-gain amp is. It's not for extra gain and is only mildly for EQ changes. Throwing a TS with low-gain settings infront of a high-gain amp lets you lower the amp gain while retaining the same amount of saturation, which cleans up the sound. The TS also lends a low cut, mid boost, and treble smoothing effect to the sound while simultaneously bringing out the pick attack in a very specific way. The end effect is that the amp is tighter, cleaner, smoother, and more suited for a modern metal context than an unboosted amp would be, generally speaking.
The Green Scream is just too exaggerated, high-mid focused, and grainy to do this as well as we could with something like a Maxon OD808, OD820, or even MXR GT-OD, Keeley TS, etc. I've used a TS808 reissue in real life with good results but can't mimic the results with the Green Scream.