Professor Gandolf says that all political systems that aim at preventing conflict are legitimate.
Conclusion
Professor G's principle must be false. i.e. At least some political systems that aim at preventing conflict are not legitimate
Evidence (since)
Totalitarian political systems are not legitimate, and
Intermediate Conclusion
Totalitarian systems are usually good at preventing conflict.
Evidence (since)
Those not in power are subject to the will of the powerful.
Evaluate
In order for this author to refute Professor G's conditional, she must supply at least one example of something that matches the trigger but doesn't match the outcome.
His principle was Pol sys aims to prevent conflict → legitimate
So she is trying to provide at least one example in which 1. a political system aims to prevent conflict 2. it is not legitimate
Her example is totalitarian political systems.
Does she establish both 1 and 2?
Not quite. She establishes that totalitarian political systems are not legitimate, but she never establishes that they aim to prevent conflict.
She only establishes that they are usually good at preventing conflict.
This is actually an example of the 11th or 12th most common famous flaw: Intent vs. Result (or Motive vs. Consequence)
Goal
So she is assuming, .
(We could also potentially see an answer linking the Intermediate Conclusion to its Premise, something like, )