I am not a lawyer. If you want a lawyer's answer, you should probably ask one. The FSF is particularly helpful in providing guidance in understanding of the aspects of various free licenses, in particular the GPL.
The GPL is a license based on copyright. The rights that copyright grant the copyright holder allow them to enforce the license.
An API is a interface - a contract. It says nothing about the code used to contact it.
Most relevant to this is Oracle vs. Google over the use of Java.
"So long as the specific code used to implement a method is different, anyone is free under the Copyright Act to write his or her own code to carry out exactly the same function or specification of any methods used in the Java API. It does not matter that the declaration or method header lines are identical."
It found that the API Oracle was claiming to be copyrighted wasn't copyrightable under section 102 of the Copyright Act.
(Yes, that's about reimplementing the Java API - but its still the most relevant thing I could find and speaks to the ability to copyright an API which is needed for a license based on copyright.)
That the company has released clients under GPL is great - it lets others use that code. If one makes use of the copyrighted code that is released under the GPL in their product, it is also GPL'ed.
The APIs remain APIs and are not (cannot be) copyrighted and thus there is no way to put them under the GPL.