I presume part of the issue here is the expression 'ride roughshod'. 'ride roughshod' is an idiom used to describe when somebeody acts without regard for the feelings or interests of others, or to act without caring about how it will effect someone or something. The term alludes to the practice of arming horses with horseshoes mounted with projecting nails or points, which both gave them better traction and served as a weapon against fallen enemy soldiers. In modern times it is used figuratively for bullying behavior.
The original article can be found here, and the article as a whole gives a somewhat clearer definition of what your key sentence means.
As you stated, the article provides examples of attacks carried out by those loyal to their own country - and the sentence points out that they act without any consideration for the way they are undermining the authority of multilateral institutions who are (presumably) trying to do good. For example:
Can the UN’s effort to fight global terrorism be taken seriously if
China continuously thwarts India’s attempts to blacklist known
If the Berlin terror attack is connected to a Pakistani national it
will affirm, once again, that country’s status as a global terror hub.