I think this needs to be said again as reading a few posts folks are still referring to their mk 4, 5 + 6 GTIs.
Previous generation golfs will not see any performance differences when increasing the octane of the fuel as they do not have variable valve timing. You cannot base your response to the OPs question on your experiences with these engines.
You need variable valve timing to take advantage of a higher octane fuel. This allows the ECU to advance the spark, burning the fuel faster/sooner and hence the valves have to keep up.
The new GTI has variable valve timing and so will see an improvement from higher octane fuel. ( the manual above is obviously an arse covering/default bit of writing )
All engines that can vary the timing of the valves and the firing of cylinders will produces more power with a higher octane fuel - up to the limits of how much advance the engine can physically produce (200 octane fuel is probably a waste)
Whether the increase in power is significant is the question. I suspect not in the new gti. 4 cylinders and 2 l only, there is not that much more energy being released. The more cylinders and the greater the volume the greater the increase.
There is no replacement for displacement!
200 octane fuel would undoubtedly shag the engine - it is aviation fuel (Avgas).
Octane rating is a measure of how far you can compress the fuel mix before it ignites without a spark. Compress a low octane fuel too far and the compression ignites it (like diesel ignition) out of sync with the engine, causing your "knocking".
Higher octane fuels are of benefit to engines with a higher compression ratio - compressing the gas further and then igniting it to get a bigger expansion on ignition. Using RON98 in a car optimised for 95 just means that when it is compressed as far as the engine will let it and then you ignite it via modified timing, you will get your combustion. A car running RON 98 when it is optimised with RON95 will be inefficient because the compression ratio will not be as high for the fuel/air mix. Less compression means a less energetic ignition - don't forget it is expansion of ignited gases which powers your car. Less expansion (because the compression ratio was lower prior to ignition) means less power. Try sitting on a balloon to pop it - it makes a bang. Try sitting on a balloon with more air in it (higher compression ratio) - it makes a bigger bang.
Higher octane fuels are all about increased efficiency in higher output engines that are designed to take advantage of the higher resistance to compression ignition.
If VW could show gains of any kind (power or efficiency) in using RON 98/99, they'd be boasting about it and encouraging you to use RON98, but letting you know that if you can only get hold of RON95 then the car will do fine with it.
I do wonder whether anyone's ever looked into sparkless petrol combustion - running the car like a diesel, purely on compression for ignition, like controlled and in-sync "knocking". Maybe petrol is a little more unpredicatable exactly when it is going to ignite under compression.