Any idea of what tasks could be prime targets for 8.4tf? AI? Physics?

Scorpio would compute at 12 Tflops?

Sorry, but I don't know details. I imagine physics requires more precision though, and there's so many different AI techniques that it's hard to say anything conclusive about it. Also, 8.4 TFLOPS is also a pretty bad phrase to use here, because it implies that all FP operations are done at half precision. That's the only way you get 8.4 TLOPS out of it. In reality, it's going to be between 4.2 TFLOPS and 8.4 TFLOPS, and it's probably going to be much closer to 4.2 TFLOPS than 8.4 TFLOPS. And since it's probably never going to be fully utilized (I don't think any system is, unless I'm wrong of course), it's going to be even less. I'm pretty sure we're talking about theoretical maximums here anyway.

This is interesting from Engadget:

'He's not exaggerating here either. In a demo this week, he pulled up a scene in Days Gone on two separate Pros and 4K televisions, one of them natively rendered and the other checkerboard upscaled. The images were nearly indistinguishable: The native game was slightly more saturated and the textures in the grass were clearly resolved while the checkerboard grass shimmered slightly in the breeze. However, from three or four feet away, it was nigh impossible to see a difference.'

https://www.engadget.com/2016/10/20/ps4-pro-mark-cerny-interview-hardware/

Basically 4.2TF is the minimum and 8.4TF is the maximum. However, to get 8.4 you will need to make sacrifices in various departments that require heavy coding.

I see indies getting more out of it or less graphic heavy games or maybe games that don't require much physics such as destruction.

A game like Destiny that has pretty much static assets and zero destruction might be able to draw on more performance.

PS4 Pro also has a feature to help with PSVR

A look at the image beamed out to the PSVR headset. Second-gen PSVR titles will be able to leverage bespoke multi-resolution technology that allows the 'edges' of the view here to be rendered at a lower resolution. There'll be a big boost to performance with no noticeable impact to image quality in the HMD.
http://www.eurogamer.net/articles/digitalfoundry-2016-inside-playstation-4-pro-how-sony-made-a-4k-games-machine

This isn't really a secret breakthrough or anything. The Xbox Scorpio and even the Nintendo Switch will be able to do the same at FP16/32

It's an extra improvement over ps4 which apparently couldn't do it yet
"Finally, there's better support of variables such as half-floats. To date, with the AMD architectures, a half-float would take the same internal space as a full 32-bit float. There hasn't been much advantage to using them. With Polaris though, it's possible to place two half-floats side by side in a register, which means if you're willing to mark which variables in a shader program are fine with 16-bits of storage, you can use twice as many.

But true, Nvidia tegra x1 already supported double speed fp16 and Scorpio will use Polaris as well.

Nintendo switch and PSVR can probably benefit more from it than ps4 pro and Scorpio. Lower screen res and no HDR require less precision. At 4K res and HDR you'll notice rounding errors much sooner. PS3 and 360 should have had this, bit late now.

Yeah, don't panic, the other consoles won't get left behind.

It has a big effect. It wouldn't apply to everything, but it's a common technique in graphics to use 16bit floats for color and lighting. It gives performance boosts on many GPU architectures.

The effect on AMD is not only doubled the throughput, but also reduces the amount of register space needed which allows more wavefronts to run in parallel and get better utilization of the GPU.