We give a proof by direct computation that at tree level, the twistor-like superstring theory in the pure spinor formalism proposed very recently by Berkovits describes ten-dimensional N=1 super Yang-Mills in its heterotic version, and type II supergravity in its type II version. The Yang-Mills case agrees with the result obtained by Mafra, Schlotterer, Stieberger and Tsimpis. When restricting to gluon and graviton scattering, this new theory gives rise to Cachazo-He-Yuan formula.