I have two questions.
[He] complained that part of the act giving police the right to break up demonstrations impeding traffic smacks of authoritarianism, arguing “it's like a law from the martial law era.”
1. No, I think an article is missing and giving is a participle that is used instead of a relative pronoun and a finite verb : He complained that the part the act which/that gives [the] police the right... The used to be very common with police in contexts like this but is less and less frequently used these days.
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