The meaning of "muted kinetics"
Solution 1:
In the world of foreign policy, “kinetics” is a euphemism for “bombing” (specifically conventional rather than nuclear bombing; derived from the “kinetic energy” of a gravity bomb). Take this quote from everyone’s favorite congresswoman, Michelle Bachman:
We should use any means necessary to bring down those who seek to bring down the United States. Additionally, Iran needs to understand that there is zero tolerance for them acquiring nuclear weapons. If I was commander-in-chief, I would eliminate their nuclear program if they refused to do so themselves. If we must, I would do so through kinetic means. I would let our enemies know: If you are thinking about acquiring nuclear weapons, don’t expect your efforts to be successful.
And “muted” simply means “softly”, “quietly”, or in a “low-key manner”. In other words
The doctrine of Israeli nuclear exclusivity was carried out in muted kinetics.
Simply means:
Whenever anyone else in the area tried to build facilities for manufacturing nuclear weapons, the Israelis quietly bombed the shit out of them.
Note that “quietly” here doesn’t mean the explosions were silent (obviously), but that the Israelis did it without lot of sabre-rattling first; without raising a fuss or making headlines, or that the action was limited in scope: the opposite of “all out” or “full-fledged” (it also sometimes means “clandestinely”).
UPDATE: Slate, The New York Post, Fox Nation, and the National Review (and, by derivation, Wikipedia) all give a broader definition of the euphemism: “active, lethal, military force”:
Slate, “Birth of a Washington Word”:
In common usage, “kinetic” is an adjective used to describe motion, but the Washington meaning derives from its secondary definition, “active, as opposed to latent. Dropping bombs and shooting bullets — you know, killing people — is kinetic.
The New York Post, “’Kinetic Military Action’ is Still Hell”
[Kinetic] simply means the use of active military force — dropping bombs, firing weapons, and the like — as opposed to things like cyberwarfare and the use of nonlethal, high-tech electronic gadgetry.
But in the context of your quote, the specific kinetic action taken was bombing (which is how it’s most often used euphemistically, because bombs have the sense of “kinetics”).