The Piyut leads up to the Ness of Chanuka. That is what we do in the Haggada. You don’t ask if the Haggada was really written for Yaakov’s Hatzala.
As to the tune, it very much matches the time period and location of the composer. It is not that different from the common Adir Hu and Almechtigger Gotte. In addition, you can see that the setup of the Piyut and the style of the tune were meant for each other.
Each paragraph consists of internal rhymes in the pattern of ABAB, BB, CC, B. The tune also starts with double, even phrases for ABAB, picks up and goes on at BB, makes an acception at CC, returning to B.