First, notice that this is an off-the-shelf testing system, not itself software that will be developed by the military or used in the missile. Should the military develop any software that runs on this system in the process of testing, that software would not be subject to the terms of the GPL by virtue of the system being GPL. There are currently plenty of examples of closed-source, proprietary software running on Linux.
But let’s say the military actually modifies this GPL system itself. GPL only requires giving up source code to those you distribute GPL software to. No distribution, no source code given up. It can remain a military secret.
The real advantage of the GPL to the military is the lack of restrictive licenses. The military can do whatever it wants with GPL software without asking anyone, it just has to keep what it develops to itself (which I believe is your whole point of not giving away technology).
It has "real time" capability, that didn't exist at this level in the open source products but until this product was developed, which is now held to the same freely distributable license.
let’s say the military actually modifies this GPL system itself. GPL only requires giving up source code to those you distribute GPL software to
All it takes is one person who legally received delivery of the software, then they can legally create as many copies of it they like, and give it to anyone they like, which is exactly how it's designed - to facilitate rapid transfer. For example, if it's provided to a (possibly temporary) US allay, they can then legally provide infinite copies to whoever they like. Surely you're aware of these mass proliferation principles the software license was specifically designed to facilitate?