Just watched the video, a lot of engines have automatic scaling checking the processors and assigning tasks to them it wouldn't surprise me if the game has unoptimized version of this so it isn't doing much with the extra cores.
Can it be solved by providing two clients - one for older machines and one for newer machines with more cores; as you reference consoles, yes it probably could.
I imagine the problem would be there would be a whole lot of deep engine work that would need to be done to make sure such a change would cause issues elsewhere.
Beyond the extra work that would need to be done, and making sure the extra client type didn't stuff up the anti-cheat I imagine the biggest issue would be the lack of engine coders who are well versed in Frostbite.
It could be a super simple fix, or it could require changing foundation elements of the engine, it would depend on what systems are in place for assigning tasks to cores / threads.
