Yes. If your application code incorporates any GPL code — and you distribute the application to run on others’ computers (i.e. a mobile app on someone else’s phone)— you must also distribute all your source code. That is really what the license says. Like I said, it’s a political statement.
Code running on a server generally evades that requirement, because you don’t distribute that code outside your own computers. That’s why the AGPL exists — when that license is in effect, any server operators using AGPL code are additionally required to distribute code that touches AGPL code.