I struggle to see how this story could not be viewed as anything other than a tragedy. Throughout the novel, Hardy makes it clear that the life of Tess, and the lives of all of us, are dictated by forces much bigger and more powerful than humans. However, certainly, the life of Tess is an extreme example of how humans become the playthings of fate and live their lives against the backdrop of impersonal forces that wish them ill. Consider the ways in which Tess is "doomed" to her fate. Marlott, as her home, perhaps indicates the bad "lot" in life that Tess will receive. There is a sense of the inevitable or the unavoidable in this novel, as in chapter after chapter, something goes wrong and fate intervenes to ruin the best intentions of the characters. The biggest example of this perhaps is when Tess writes Angel a letter describing her past, but pushes it under the mat so that it goes hidden. The tragedy of this novel is that Tess is reduced to a plaything of fate. The quote you originally included in your question makes this clear:
'Justice' was done, and the President of the Immortals, in Aeschylean phrase, had ended his sport with Tess.
The sense of tragedy is exacerbated by presenting Tess as a helpless creature in the hands of forces much stronger than her. Her tragedy has nothing to do with her own actions or character, but is the responsibility of fate, which is presented as a malignant force that exists in an evil world.