If a software is GPL licensed, any future variants of the program will automatically become GPL licensed as well, regardless of what you created and put into it. And anyone who run or interact with that code in any way must have access to the source code.
It is the definition of free software. If you do not provide people with the source code, they can not know what the software does. Anyone means anyone. If you sell a modified version of The Forgotten Server, you have to provide the buyer with the source code. If you plan to host it publicly (meaning, not privately) you have to provide access to the source code to all players.
Public is the opposite of private. As soon as you either sell it, or have code that is run or interacted with from another person's computer, it is considered public use. And if it is GPL licensed, that person must be provided with access to the source code. Especially with GPL 3.0 licensed code, but also GPL 2.0.
Since 1983, developing the free Unix style operating system GNU, so that computer users can have the freedom to share and improve the software they use.
www.gnu.org
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I can not make things clearer for you. If a computer program is GPL 2.0/3.0 licensed, it must conform to the free software guidelines. Any and all future copies of it will remain with the same license. Because it is free software, it must include the "four essential freedoms" listed in the image above. If it does not do that, then it is a violation of the license.