Neoclassical economics suggest moving up the price ladder. But as a comment above mentioned, STEM job supplies are quite inelastic. In fact we should expect it to be inelastic, since STEM jobs require more expertise than say general labour.
there are other options any fixed price x(i): no trade (not one), and equilibrium (no more). If X is floating, the question is different. Then its a question of why X wages are not enough. Its also a question of why the jobs are not made better (not everything is price related, the firm is a hierarchy...). etc.
I don't know how much of that money goes to engineers, but I do know that more than a handful of my engineering friends have been lured to defense. It would be interesting to a study that tried to quantify the distortions, though.
Employing engineers in defense has the opposite effect of a subsidy: it takes engineers out of the commercial job market thereby decreasing supply and raising prices.
From that wikipedia article you linked: "In standard supply and demand curve diagrams, a subsidy will shift either the demand curve up or the supply curve down. A subsidy that increases the production will tend to result in a lower price, while a subsidy that increases demand will tend to result in an increase in price."
Defense R&D increases the demand for engineers and thereby raises their "price". I don't know if it has a significant effect though.
The government employing engineers is strictly speaking not a subsidy. It's just an increase in demand. Yes, one type of a subsidy does result in an increase in demand. But causing an increase in demand is not a necessary&sufficient condition for being a subsidy. Because now the government is demanding engineers. It does not decrease supply. Someone who is employed is still by definition part of the labor market. The only person who is not a part of the labor market is someone permanently not looking for work.