I don't read it that way. What the author is against is using parameters for the specific purpose of controlling the flow of a function. Instead, the author recommends breaking the function up into as many functions as there are variants of the type key.
This also applies to boolean flags (where only two variants are possible). There are, of course, exceptions as the author points out.
The small win is that the type key no longer needs to be maintained. The big win is that each function that gets split out has fewer reasons to change. The individual functions are therefore easier to maintain and understand.