It's a pretty interesting question, even if a bit tangential to the article!
Their main advantage is the comparatively low transistor count. The chips can be made cheaply and don't need cutting-edge fabs. This also makes them exceptionally power-efficient and tolerant of a wide range of supply voltages, so they're easier to integrate into many designs.
Just as important, they are far easier to master. Single-cycle instruction execution, single chip-wide clock, simple interfaces to all peripherals. If you don't have an OS to abstract it all away, most of the contemporary 32-bit platforms are a serious pain. Adjusting clock speed on a typical Cortex-M chip requires following a carefully-choreographed sequence of steps, possibly fiddling with flash wait states, various bus clocks, PLLs, and so on. On an 8-bit MCU, you just flip a bit or two.
It's a weird misconception that "8-bit" means antiquated or slow. Modern 8-bit MCUs run at high speeds, have plenty of fast memory, and integrate all kinds of cool on-die peripherals - DACs, ADCs, op-amps, DMA controllers, USB controllers, and so on. And in a good majority of embedded applications, they are enough.
Of course, there's nothing sacred about 8-bit ALUs, so I wouldn't be surprised if 32-bit ALUs eventually take hold in this market segment. But the replacements would need to preserve that "I can learn this in a weekend" property that isn't preserved in most of the high-performance 32-bit chips available today.