You are looking at the problem from a wrong angle.
There is no chemical reaction* taking place here. The only thing that matters are intermolecular forces between the activated carbon surface (which is mostly just a naked, raw carbon lattice layer, like the one present in graphite) and the dye.
What you got as a structure of the activated carbon is just an example of what can go on on the border, where the lattice ends. It doesn't play any role in the absorption process.
*A lot depends on how you define the chemical reaction, as there is no strict border between what we simplistically classify as chemical and physical processes, instead there is a continuum of processes. Nature doesn't care about our classification attempts.