Yeah, I'd expect some sort of artifacting with moving objects in their upscaling, I guess that's what it'll look like. The real test is whether it's noticeable in motion, since those artifacts will only last for a frame if I'm understanding the upscaling method. Considering ghosting is still a thing on modern TVs, it might actually not be that noticeable.Lara's arm is ridden with artifacts on the PS4P here.
I mean, in the cropped image of the rock (which is presumably static in the frame), PS4P is pretty much as sharp as 4K. If the artifacting isn't too noticeable, then I mean, that's good enough... for an affordable 4Kish gaming console.
Edit: I don't wanna sound judge-y, but since the advent of shaders, I've always found it kinda silly when people try to make IQ judgements using screenshots.