It might be two separate usages of the term "Qualified"
1) If you saw it first on the page "Where is this distribution from?"
That page is used by the state..
Where you selected a bullet point....then it's probably a somewhat mis-usage of the term by the state
...a better term for that page might be "Eligible Government Retirement Distribution".
........meaning is that distribution eligible for exemption/exclusion from your state's income and thus may not be taxed by your state..
2) The second page is a Federal question....DFAS military pension payouts come from what are considered non-qualified plans. Apparently it is one that does not meet ERISA ( Employee Retirement Income Security Act of 1974) guidelines....and DFAS Military pensions are not.
However, TSP distributions are qualified Retirment plans (for the second page question), and is exactly equivalent to a 401k.