Same entry in other lexica, and cf. also the scholia to Thucydides 2.49.1, where the headword appears -- of all other illnesses, in Athens in 430 BCE, becoming the Plague. (This is neuter plural with a singular verb, which needs translating as a plural.) For a)pokri/nesqai in this and other medical senses, see LSJ s.v.
Thucydides is here using a common verb in an uncommon way. Typically of his complex thought-processes, he is compressing two ideas into one: (a) that the illnesses which beset Athenians at this time began by appearing as a variety of illnesses but all ended up as the Plague, and (b) that by so doing they were collectively a special category of illnesses.