It would be nice if you told us where Dawkins said that so we could put it into context.
None of the hemoglobin found in "annelids, echinoderms, some molluscs, some arthropods, etc." are chemically or structurally the same as any of the human hemoglobin. Nor is that in yeast and beans the same. Many times the protein is not true hemoglobin but only "hemoglobin like". Others are monomeric globin. The hemoglobin found in vertebrates is unique to vertebrates. However, the source of all of these may be an ancestral myoglobin.
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