it's poetic license.
It adds to the overall image of someone in extremely casual, if not actually scruffy clothes - & who doesn't care about it.
The headline of the article you linked gives that away right at the start…
The leader of India's newest party, Arvind Kejriwal, is known for his austere lifestyle and simple clothes.
… and goes on entirely about his sense of 'style' or lack thereof. It barely mentions politics at all.
His shoes are dusty. He is relaxed. The addition of 'relaxed' to the description of dusty shoes gives the feeling that this is not a new or temporary condition for his shoes; it is how they always are.
The combination of the two ideas is imaginary, yet conveys the imagery of his lack of concern with his visual appearance.
An aside - dust could also be described as agitated, disturbed, angry, insidious - all of which are anthropomorphic terms to give the idea of some kind of emotional state to an inanimate substance.