How can Romanticism be defined in “The Poor Singing Dame” by Mary Robinson?

Robinson's "The Poor Singing Dame" can be defined as part of the Romantic tradition for a number of reasons. To begin with, in its opening stanzas, it makes abundant use of the Romantic trope of nature celebration, with the countryside in which the titular old dame lives being described vividly; the "summer sun" shines on the "rushy roof" of the woman's house, and "sweet birds" chant above it. We see personification in the depiction of how "the tempest would roar" upon the house while it, itself, "defied the wild winds." Moreover, however, we also see pathetic fallacy, in which the behavior of nature or the external environment reflects what is happening in the internal environment. Here, the defiance of the old woman's little house, and the fact that "sweet birds" choose to grace it with their presence, stands in contrast to the grim castle which is "haunted and dreary." The external landscape of the old lady reflects her internal constitution and her worthy soul, whereas the castle, as an external manifestation of the man who lives within it, is cold and unappealing. This is a common trope in Romantic and early Gothic literature, and here foreshadows what will follow in the poem. It is particularly notable that the old lady is associated with nature's abundance and "sweet music," which the lord of the castle hears and is enraged by. The old lady is happy in her environment in summer and winter alike; she "carolled" in the woods even when winter's frost lay on the ground, which the lord of the castle cannot stand.
The structure and tone of this poem suggests pastiche, a deliberate imitation of the ballad form which seems to set it in a quasi-medieval past time, another common trope in Romantic literature. The concerns of the poem, however, revolve around the idea of tyranny against the poor, which was a primary focus of the Romantic poets and which reflected topical concerns at the time of writing. The lord of the castle, the poet says, "hated that poverty should be so cheerful." His idea of poverty does not include its being a happy and content natural state; instead, he is resentful that the old woman seems to be free of cares, and he sends soldiers to bear her "all trembling, to prison, away."
Tyranny, the poem suggests, is born out of the basest of motives on the part of the rich: largely, the idea that poor people are not entitled to be happy. However, even after the old lady dies in prison, nature continues to be on her side. "Primroses" spring up to mark her grave, while "breezes...bid the fresh flowerets in sympathy wave." The old lady continues to be at one with nature, even in her death, while its manifestations express sympathy for her plight. Her external environment continues to reflect her purity of heart.
Meanwhile, the lord finds that "screech owls" visit him every night, "hooting a terrible song" and haunting him day and night. Eventually, he is overwhelmed with shame, and

the tomb of rich marble, no soft tear displaying, O'ershadows the grave of the poor singing dame!

The tyranny of the rich man in the poem, then, not only causes him to literally "decay" from shame at his own misdeeds, but sets him out of place in nature to the extent that nature attacks him. In this poem, as in many Romantic works, Robinson draws a connection between the deserving poor and the idyllic nature of the countryside, a birthright from which the industrial revolution had separated them. Meanwhile, the rich are associated with a destruction of nature's ways, a perversion of what should be. Tyrannical behavior warps the way society should function and will eventually, the poem suggests, rebound upon the oppressor.