For a single-rate filter, a 2 Gsps input sample rate also means a 2 Gsps output sample rate. Because the input stream is separated into two (even, odd) streams, the output stream must be split the same way.
Take a look at how y0 is computed:
If the data stream is split into two phases, it can be seen that the coefficients also have to be split into two phases.
Also take a look at how y2 is computed: