We know what happens during normal brewing, so we can look at what the increment in time and temperature for extreme brewing does to the composition of the coffee brew.
About 30% of the coffee bean's weight is soluble compounds. The compounds have different solubilities, so they dissolve at different rates. The first roughly 20% of the bean to go into solution is good tasting stuff. The last 10% is bad tasting stuff. So normal coffee brewing is designed to stop the extraction after getting out the good stuff. If you brew longer and hotter, you can extract that last 10%. After that is in solution, there's nothing left to extract, no matter how hot or long you brew it.
What studies there are on health benefits generally look at potential benefits from what's in coffee brewed to be drinkable. Those studies typically compare coffee drinkers to non-drinkers, look for correlations with amount of coffee consumed, or look at specific compounds in normal coffee that might be promising.
The compounds that dissolve during normal brewing get mostly extracted by normal brewing. Brewing for a longer time or at a higher temperature might extract some small additional amount of those.
As quoted in the question, those compounds can be affected by high temperatures. But even boiling temperature doesn't compare to the high heat during roasting. Any chemical breakdown from heat will have already happened during roasting. At brewing time, the water temperature primarily affects how fast those compounds go into solution.
So whatever health benefits there are from what is in normal coffee would not be affected by extreme brewing (other than your ability to still drink it to get those benefits).
The main effect of extreme extraction is that it adds some other compounds (the last 10% to dissolve). There is not much incentive to study those compounds for health benefits since nobody consumes them, at least in coffee. A possible exception would be tannins, which you also get in tea and other things. The research on tannins is mixed (good and bad).
Keep in mind that knowledge about health benefits isn't fixed. As you get more research, the conclusions can reverse. That has happened with tannins, for example. Research has repeatedly flipped whether it is good or bad (see Tannins and human health: a review. Research on health benefits continually evolves, so you shouldn't bet the farm on what might look like benefits today from coffee at any specific extraction level (or pretty much anything else). If you never saw the 1973 Woody Allen movie "Sleeper", he wakes up in the future and everything that people thought would kill you turned out to be good for you; everything that was thought to be healthy turned out to kill you.
But if you wanted to investigate the potential health benefit implications of extreme brewing, the way to do it would be to look at the compounds in the last 10% of solubles and the research that is available for them.
If there was something known to be especially healthy in the last of the solubles, people would be extracting and using it. It tastes awful, so using it might be in pill form, or adding it in small amounts to something that would mask the taste (or making "industrial coffee" that you mask with copious amounts of creamer and sweetener). The fact that this doesn't happen (well, the industrial coffee happens, but not for the purpose of health benefits of over-extracted coffee), suggests that either there are no known health benefits from it, or there isn't enough of the beneficial compounds in coffee to make the extraction worthwhile.
