"So, in the 'definition of a programming language', what makes PHP not a 'proper' one?"
The real reason is the fact that most people do not use it as a general purpose application programming language.
It is because there have been always languages which are better suited (with one exception: what PHP was created for, web programming). PHP is "yet another language not even with better design features over existing ones". Some examples of issues when comparing to different other languages include: lack of stable and portable GUI toolkits (at least on Windows/MacOS), lack of threading, lack of speed, and so on.
Ultimately, people who are going to write general applications in PHP, are mostly people who only know well PHP as a programming language. Because there is no reason to write a new application from scratch in PHP: you'll find that most experimented or talented programmers would never consider doing this.
