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To the best of my knowledge the Z06 doesn't have one, and it has more power and corners harder, so need might be a strong word. Maybe they think it looks good and might do something. Maybe their streets are really bad.
In all seriousness, I highly doubt it does anything but I suppose it does look neat. I've added chassis bracing on other cars that actually needed it and the improvement has been noticeable, but I'd be shocked if the C8 falls into that category.
If it were to actually do anything though, that design wouldn't be it. I could flex that thing with my hands! You'd want to box in that design at the bare minimum. The Honda S2000 actually did need something similar to this, but it was mounted underneath the engine. Whiteline and Spoon were considered two of the better designs.
1-2mm is negligible flexion IMHO. I doubt you will feel any difference in the moment when this might help. Looks cool I suppose, but if you are looking for aesthetics, I love the look of those cross braces on the ACR. Flattened oval tube vs a round tube.
This doesn't seem to really add much rigidity to the existing structure. It would be much better made from a square tube and also needs a cross brace in addition to the central connection point. Looks structural and IS structural are not the same things. It's also very thin so again it's adding very little. It's also seemingly unnecessary and is just adding weight for no return.