Recombination current in general is defined as current that occurs
when an electron and a hole with a small amount of
kinetic energy meet and, as you mentioned, these electrons contribute to the overall
current flow.
However, it is important to remember that electrons and holes are everywhere inside the transistor. There is, of course, a bunch of holes in the p-type base region, but there are also some in the depleation region as well. However there are so few that one can get reasonable accuracy out of their model even if they ignore it. If you want better accuracy out of the model then you don't get to ignore it anymore.
So for this model, equation 5.2.13 defines the base current as:
I_b = I_e,p + I_r,b + I_r,d
Where
I_e,p : The hole diffusion current
I_r,b : The base recombination (the mechanism you describe but occuring only in the base)
I_r,d : Recombination current in the depletion region (same mechanism different spot of the transistor but the electrons ultimately come from the same place)