How does this poem relate to the Victorian Age?

The first thing most readers would probably identify as "Victorian," though it really applies to any time before the twentieth century, is the rather dictatorial attitude of the Duke as he describes the Duchess's "faults." The Duke's chief complaint appears to be that he was not the absolute center of her universe, that

. . . she ranked
My gift of a nine-hundred-years-old name
With anybody's gift.

The Duke, fed up with this attitude of her seeming beneficence towardseveryone, then resorted to openly ordering her around:

. . . I gave commands;
Then all smiles stopped together.

In the end the Duke seems to have thought her idealization by the painter, Fra Pandolf, as no more significant that the Neptune "which Claus of Innsbruck cast in bronze for me."
Browning, of course, is critical of this male chauvinist stance, as many progressives of his time were. But apart from the gender-issue element in the poem, to me what typifies it as "Victorian" is the fact that the backdrop of the Duke's monologue is Italy. Browning, like many other British and American writers of his time, was fascinated by Italy, which represented an ideal land of art and warmth, a haven to which people of artistic sensibility were inevitably drawn. He moved there with his fellow poet and wife Elizabeth Barrett Browning, living there with her until her death in 1861. Other works by Robert Browning—his long debut poem Sordello, the dramatic monologues "Andrea del Sarto," "Fra Lippo Lippi," and others—show a fixation on Italy as a kind of sun-kissed paradise, an escape from both the gloomier skies of England and the stricter morality of Northern Europe.

In this poem, the Duke reveals that he treated his deceased wife as if she were a piece of property he owned. The poem was written in 1842, and the status of the Duchess reflects the status of women in England during that time period and throughout much of the Victorian age. Until the passage of the Married Women's Property Act of 1882, a woman lost her legal personhood upon marrying. At that point, she was considered merged or of one flesh with her husband. Since they were considered one person it was a male-dominated (patriarchal) society, all the wife's property became the property of her husband. The wife herself belonged to her husband. She was expected to be obedient to his will and could not dispose of her own property without his permission.