This is explained in the GPL FAQ section "Does the GPL require that source code of modified versions be posted to the public?".
The GPL does not require you to release your modified version, or any part of it. You are free to make modifications and use them privately, without ever releasing them. This applies to organizations (including companies), too; an organization can make a modified version and use it internally without ever releasing it outside the organization.
But if you release the modified version to the public in some way, the GPL requires you to make the modified source code available to the program's users, under the GPL.
Thus, the GPL gives permission to release the modified program in certain ways, and not in other ways; but the decision of whether to release it is up to you.
In the worst case, the server code will have to be open source and free to use for anyone it is being distributed to. So when they give that server software to someone else, then that someone else has to receive it under the terms of the GPLv2. But when they only use it themselves on their own servers, then they can keep the sourcecode and rights to themselves.
Using a software by connecting to it via network is not considered distribution. That's a loophole covered by the AGPL license.
For more information on how the GPL works, I recommend the GPL FAQ.