In fact, at least PPC and MIPS (at least as of a couple of years ago) are also in the running for 2nd and 3rd largest CPU architecture in termsof number of CPUs - but as with ARM they're dwarfed by Intel in terms of revenue, as all three have a licensing model and target markets with much lower price per unit than what Intel does.
There are other potential architectures up there, though primarily used as microcontrollers, but getting accurate numbers is very hard.
Getting reliable numbers for the CPU market in general is annoyingly hard. I'd really like to see how the numbers for PPC and MIPS are developing.
Also older CPUs that are now treated as microcontrollers, like Z80 and 6502 descendants.
Western Design Centre has a statement about annual volume in the hundres of millions for 6502 descendants on their website [1], which if true means it's somewhere in the same region as MIPS, PPC and x86 for one of the top 4-5 spots after ARM.
RISC is better in low compute power. CISC is better for high compute areas.
The interesting, high-growth spaces where ARM and Intel are currently battling for hardware mkt share are the IoT Gateways market and the autonomous vehicle SoC market.
The supporting software ecosystem will also become increasingly important over the next few years - this is a spot where ARM could really outpace Intel if it receives a big infusion of resources (see ARM mbed cloud/OS).