Does the Savage ability of the Lizardmen go on the chain?

An example: My opponent plays Master Rune of Spite and my Carnosaur Riders trigger to kill the Rangers in the Quest zone.

My question would be: Can my opponent react to the Savage ability of the Lizardmen or doesn't the ability allow other abilities to enter the chain as if it was a forced effect?

To me 'savage' looks like 'counterstrike' in the way its printed on the card. It seems to be a constant so that nobody can respond to that.

See faq:

Q. Can I respond to my unit taking counterstrike damage, e.g. by sacrificing a unit to Grudge Thrower?
A. No, you cannot respond to counterstrike damage (rulebook, p16).

It is not an constant effect, it is an triggered keyword.

I am sure that you at least cant do actions between assign and apply because Savage is Non-Combat-Damage.
Going on the stack? Probably not.