Not all computing machines use temporal pulsing. Turing machines don't.
What is more, not all computing machines perform all steps in order: asynchronous circuits don't. Distributed systems don't.
I believe the author is mixing up
- computing as a discrete (stepwise) process
- strictly sequential computing, in which no steps are executed concurrently
- clock-based computing, in which steps happen in sync with a clock
You often have the first without the second, or the second without the third.
Modern CPUs use pipelining, in which steps do not happen in sequence.
Modern software systems use pipelining in the large, in which multiple data processing units are combined into data flow networks or other types of communicating computational systems.
Strictly sequential, one-processor, one-instruction-at-a-time computing is conceptually simple and therefore attractive to theorists, educators, and people who want to build simple systems. Turing machines work that way. They are an example of the second type of system; they don't involve time, but they do perform their steps in strict sequential order.
As galdalf61 writes, the notion of algorithm is often limited to such strictly sequential computation. That doesn't mean actual computational machines or systems all work that way; they don't.
Similarly, basing everything on a clock makes digital circuitry easier to design, and it happens often, but not always.