You cannot charge extra for distributing source code in this way under the GPLv3 (or any version of the GPL, for that matter -- there is a carve-out for physical distribution that lets you charge for shipping, but that doesn't apply here). Section 6(d) explicitly says this:
> You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: d) Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. [emphasis added]
That bit in the FAQ is describing the situation where the software binaries are being sold for a fee -- in that case, the GPL only requires you to provide the source code (for no additional fee) to the customers that bought the software from you. In fact, is the case in general that the GPL only requires you to provide source code to the same people you gave binary copies to -- the FAQ is just clarifying that that GPL does not require you to publish source code in public (the FSF considers such licenses to be non-free). This game is available for free to the general public, so this situation (and the text from the FAQ) do not apply -- they need to provide the source code to everyone that they distribute the binaries to.
The need to disallow charging extra for source code is obvious -- if distributors were allowed to charge for source code, they could fork a GPL project and then charge $1B for the source code, making the code effectively proprietary.