What's Victorian in "Dover Beach" is, of course, the sense of spiritual loss and doubt. However, in addition to those, several things make this Victorian. First, the mix of continuity and failure. By that I mean, Victoria was on the throne for a long time; this creates a sense of continuity. However, many of the institutions of British society are failing or changing. Second, the re-use of classical references to new ends, such as commenting on Arnold's own society. Third, Arnold's own poetic theories. Arnold argued for higher culture as a way to replace the lost faith he comments on in the poem. The poem itself is exchanged between two people who stand apart from the place "where ignorant armies clash by night," much as the bastions of higher culture must do for the ignorant clashes of mass culture."
What is most Victorian about this piece is its sense of spiritual doubt. While the Victorian Age (1830-1901) is primarily viewed as a time of great progress and the attainment of world power for England, there were also serious spiritual doubts beginning to take hold in the culture. Much of this can be attributed to the rise of scientific theories that no longer included a "creator" such as Darwin's theory of evolution (The Origin of Species was published in 1859). In the face of his doubt, the speaker in "Dover Beach" suggests that human love may be the only substitute for this kind of spiritual loss.