The Maharil also notes the gematrias. The reason is that during the middle ages, a question arose as to why the author of the piyut deviated from the order of the 3 actions as stated in the Talmud Bavli (I don't have the source or quote handy). Some tried to change the order around in order to match the Talmudic sources and others felt the need to preserve the text of the piyut as they had it. The point made by those gematrias is that, in fact, all three actions are equal and they shouldn't change the order.
In fact, the piyut's composition predates the Talmud, a fact that the medieval authorities were probably unaware of. More on this here: http://www.yutorah.org/lectures/lecture.cfm/747445/Rabbi__Kenneth__Brander/UNetaneh_Tokef:_Understanding_the_MartyrologicalIn fact,_Midrashic_and_Talmudic_Roots the piyut's composition predates the Talmud, a fact that the medieval authorities were probably unaware of.