It's all very simple. Islam is a unique religion in that its main prophet had military chops and there are specific surahs that suggest that fighting well gives you a reward and is a sign of being righteous.

So any competent general has de-facto political legitimacy and is a de-facto threat to whatever government is in place. Most of the leaders in the region know this and as a result armies are staffed with insiders (which the article notes).

Saudi airforce is basically a jobs programme for elite families.