SHRUGGISH is not a real word. It just means related to or like a shrug. And a shrug is the gesture of indifference.

He did not care at all.

The verb "to shrug" means to raise your shoulders in a way that shows that you don't care. "Shruggish" is making an adjective out of that verb, although I don't think this is an actual word. The sentence means "he listened in a way that showed he did not care."