Intel's dominance in the world of microprocessors remains unabated and should persevere for the next decade despite stiff competition from AMD, ARM, and potentially some new players. The demise is in mind share, especially with the whole idea about microprocessors and the x86.
The x86 era is over because the public stopped caring about it when Apple introduced the first poke-and-shove GUI on the original iPhone in 2007.
This was compounded by the trivialization and redefinition of software as "apps." These changes made all levels of computing eventually more approachable but also dumbed down the entire scene to the point that nobody in today's market really cares how anything works.
This public divorce from mechanism actually began before the poke-and-shove interface. It was realized during the wishful thinking ethos of the 1990s when people wanted computers to become appliances. Computers would be so simple that anyone could use them with little fuss. I always thought that this idea stemmed from a general laziness on the part of the public, who wanted nothing to do with understanding computers. It was too much work.