In this example, do you think the speaker of the quote was using it in a negative connotation? I think it's pretty clear that that is not the case.

Precisely. The speaker might happen to be "a bro" in the derogatory sense of the word (especially given involvement in an activity that may have a significant population of those people), but that's fairly distinct from simply calling someone "bro" as used in this quote. But I do say "fairly" because bros (in the derogatory sense) probably also call each other "bro" (in the sense that someone is close like a brother) at a rate that exceeds baseline.