The entire point of the argument is that perl doesn't first completely parse the program before it runs it. When executing a Perl program perl alternates between parsing and running. That's what BEGIN is about (and hence, use).

The article proves that it's actually impossible to do otherwise. That is, there does not (and will not) exist a program that first completely parses a Perl program, then executes it. (Well, at least not as long as Perl remains as it is).