Attached are the first four hops that all traceroutes from my computer show:

  1    <1 ms    <1 ms    <1 ms  192.168.1.1 
  2    23 ms    22 ms    20 ms  7.4.0.1 
  3    23 ms    23 ms    24 ms  7.3.0.1 
  4    24 ms    24 ms    23 ms  216.58.163.10 

Now, I understand that 192.168.1.1 is my router, and I know that
216.58.163.10 is my upstream provider here in Colorado.  My question
is, why are all my packets going through two DoD computers in Virginia
in between my router and my provider?

I believe it isn't showing two DoD computers; but your service
provider has elected to use addresses associated with DoD computers in
its internal infrastructure, and the path from your router to the
Internet passes through
those elements of the ISP's system.