I see Dharma as a thing with many layers, as well as many different interpretations. Textually, it is defined as "carrying out one's responsibilities and duties" (95) but I see it as less of the action itself, and more of the morality or spirit in which you carry out these actions. For example, since there are multiple types of Dharma, with some encompassing all people, and others being individual, there are many common applications of it focusing on the spirit. For the different social classes of the caste system, there would be different ways they are expected to approach fulfilling their responsibilities depending on where they are in the social hierarchy.
The main reason I think Dharma is so important in Hinduism and is focused on so much in the Rāmāyaṇa due to how differently people understand it, therefore how applicable it is to so many different aspects of life. Dharma is said to span "the duty, natural law, social welfare, ethics, health, wealth, power, fulfillment of desires, and transcendental realization" (73) With Dharma being relevant in all of these different topics, it is clear why it is as prevalent in Hindu life and in the text as it is.