Beckett has been reported saying: "I am not unduly concerned with intelligibility. I hope the piece would work on the necessary emotions of the audience rather than appealing to their intellect." In other words, Beckett was more interested in how the audience felt and reacted rather than being concerned about whether or not they eight-minute short play made sense on an academic or intellectual level. In addition, the use of language in the play is at best sparse and symbolic. In these way I would argue that the play squarely fits into the genre of Theater of the absurd. For more information on theater of the absurd check out this academic website: http://www.arts.gla.ac.uk/Slavonic/Absurd.htm.
The generic positions in Beckett is a very complicated issue. if one allows this simplification of sorts, I think what Joyce does is to create a multi-generic work in Ulysses or Finnegans Wake, but in Beckett's works, especially the late works, there is a breakdown or an internal transformation of genres. It all becomes one pure-genre. The prose becomes poem. Theatre becomes poetry.
Rockaby is verse-theatre. Ruby Cohn and Enoch Brater call it a 'performance poem'. It also uses a Ballet-like rhythm of the rocking chair which corresponds to the speech-rhythm of W. It is an intensely musical piece where speech is turned into pure sounds, to be understood phonemically rather than semantically. It can also be called a 'dramaticule', the term with which Beckett himself classified Come and Go. The play, in a typically Beckettian way, turns theatre into a stage-image beyond anything else and the onstage character listening to an offstage voice is a stock Beckettian situation in the dramaticules which are not just minuscule drama but dramatic ridicules in the sense that they redefine the very notion of theatricality--what can be performed and what cannot be. It is a minimalist drama per excellence and the operative ideology behind it is one of the Avant Garde experiment with speech, silence, performance and semantic suspension.