More likely is they start requiring selection of open source products for critical government programs, including defense, where the source code is released under a license that allows infinite copy and distribution after a single purchase by anyone:
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).