It is a variant on Eugen Sänger's antimatter rocket. One of the key difficulties of harnessing the energy from matter/antimatter collisions is that most of the energy released by them is in the X-ray and gamma ray spectrum. The redshift rocket proposes to use particle beams, such as those produced by ultrafast laser pulses. Both the matter and antimatter would be accelerated to near light speed away from the spacecraft before colliding in the reaction chamber. This would lead to the radiation that reaches the spacecraft being redshifted. If the speed of the particle beams is great enough, the radiation that hits the spacecraft will be of a frequency that can be reflected. Energy absorbed by the spacecraft could be used to help power the particle beams.
But as a result only a very small fraction of the matter/antimatter annihilation reaction would contribute to the propulsion and the main source of thrust would be the particle beams themselves, which must be generated by other means.