If i take a web application which is subject to GNU/GPL license and modify it in-house and then use it as a subscription fee business model, for eg. user pays for service and web content and not for the software itself, thus i am not distributing the software itself, is my custom version of the software be subject to the GNU/GPL terms of redistributing the source and the same terms or not?

To give more in-depth to the issue, let's take for eg. a web game licensed under GNU/GPL.
If i take it and modify it and add content and custom gameplay and such to it and then host the game with a subscription fee or free but with in-game purchase model. In this case the user will pay for the service itself of using the online service/server and gameplay/content. Will my custom game infringe the GNU/GPL license model of the original source and be required to release the modified source under the same terms?

As for the subscription based business model for charging for services and not for the software itself, i know that it is not infringing the GNU/GPL model, thus totally possible, unless someone contradicts me? Thus i am more interested in source code releasing part of the issue.