The American novelist, John Irving, said about his work The World According to Garp, that it is a life-redeeming work in which everybody dies. Comment on the extent to which the same might be said of Hamlet.
Redemption may not be of enough magnitude to be a theme, but it is a trope as Hamlet continually redeems his reason in his deliberations with himself. Then, too, in the end, Hamlet does redeem Denmark as he rids it of the "something rotten" that has been the Danish court.
"Redemption" has many different meanings ranging from (1) to buy back or ransom as in something that was in captivity (2) to recover ownership (3) to fulfill a promise or a pledge. So in one sense, Hamlet is a play of redemption because Hamlet does in the final analysis fulfill a promise or pledge to the ghost to avenge the death of his father, King of Denmark. In another sense, it is not a play of redemption because Hamlet did not recover ownership of the throne of Denmark on his father's behalf.
The most common sense of "redemption" is that used in religious discussions. It means to be delivered from sinfulness by a sacrificial payment made by one person for another, guilty, person. Unless Hamlet's death is viewed as a sacrificial payment made by Hamlet for Gertrude, Ophelia, Polonius, and/or Claudius's redemption, then this redemption does not seem to be a factor in the play. Although, it may well be that Hamlet's death was sacrificial redemption for Gertrude and Ophelia, with self-directed redemptive sacrifice for Polonius's death.
I would not call it a story of redemption. The only character who needed redeption-- Claudius-- does not earn it. Every other character who dies has no need for redeption. They were justified in their actions, for better or for worse.