Good question! Which is why I already wrote reflections on exatly this topic:
Basically my take is that Intel and AMD are put in a catch-22 situation: If they want to get ahead of the game they make their own ARM microprocessors.
Now if those ARM processors are great they can outcompete outer ARM makers. However that also means they cut the legs of their own x86 platform which they currently dominate. Hence they are in danger of undermining the very platform which is their cash cow.
On the other hand if they don't make ARM processors, they risk getting too far behind by the time ARM takes over the market.
Many businesses have been in exactly this bind in the past, and it is very hard to navigate out of. That is why is make some comparisons in my story about the transition from steam locomotives to diesel locomotives as well as the curent transition from gasoline cars to electric cars.
There is undoubtedly a market transition from x86 to ARM. The question is how the established players are to navigate this transition. IBM never really managed transition from mainframes to PC.
NOKIA did not manage transition from feature phones to smart phones.
Microsoft Windows will likely survive this transition better than Intel I think. AMD I am unsure of. They seem to be quite forward thinking and have already in place plans for ARM chips. If AMD jumps ship first, they may be able to survive.
If they utilize their current rising success in the x86 world to venture into ARM, they may be able to stay relevant for the future. Since they have strong GPUs, I think they are better setup for the future SoC world.