The word translated here 'beast' literally means he is dumb, and it is talking of any animal he may keep, whether it is a cow or a horse or a camel – his dumb beast. The point being made here is probably stronger if you bring the word dumb back into it because then you get this sense, a righteous man is sensitive to the needs of even his beast who cannot speak and express them.
This is to do with the inner life. How capable I am of thinking, embracing, perceiving needs, how sensitive, how feelingful I am. What a tragedy if I am a Christian and yet I am as blind and deaf as they come. I do not register anybody's needs; I am not sensitive to anything. I can just tread on everything and never respond or react. Why a righteous man is sensitive even to the dumb beast, let alone to his family, his wife, his neighbours, his friends, and the unregenerate – the people he works with and so on.