(I'm British and so not a US tax payer, just a spectator, but would argue the same here)
It's a crying shame the F-22 production line was shut down, so it's great to see it performing well.
(Speaking as a DCS sim pilot with a long time interest in military aviation).
Clearly a baloon is so hard to dispose target that making sure the aircraft indeed can be up to this task is worth any money!
Although the X is an all aspect missile, the parameters would still be quite different.
I think this is would all be firmly in the "not public domain" bucket of details though, as I haven't seen much of this modelled in DCS.
(I suppose they could also have used eg a radar guided AIM-120, but they are primarily for BVR, more expensive at ~$1.1, and far, far more scope for erroneous target locking, so why risk it when the 9X obviously gets the job done. Again, from the point of view of an armchair - or a rig to be precise - sim pilot. I claim no credentials beyond this interest).
Air to air missiles cost on the order of $300,000.00 weather balloons cost and order of magnitude less.
We'll all have bigger problems if that day comes than the pesky billion or two it will cost from the US $773B DoD budget.