The required sense of “severally” is:
severally, adv. 1.a. Separately, individually; each of a number of persons or things by himself or itself; each successively or in turn.
Oxford English Dictionary.
So the translation says that instead of the chorus singing in unison, or a single chorus-leader declaiming the whole speech, the individual parts of the speech should be performed by individual chorus members.
Just as actors can adopt the medium of the chorus in a kommos and a monody, so the chorus occasionally speak. Editors usually assign their dialogue lines to a single coryphaeus, or chorus-leader, who takes on the role of group representative, as in the Furies’ cross-examination and dialogue in the trial scene of Eumenides. At other times, however, we hear various voices from the chorus, as in the exchange after the death of the king in Agamemnon, when each member speaks his view on the best course of action. Lines also may have been divided among different speakers in the more conventional utterances of the chorus, such as identifying new arrivals, bidding farewell to departing characters, offering a short break between long speeches, and helping the audience to follow a change in principal speaker (difficult in a large theatre with masked actors) by interjecting a call for moderation between the two contending parties.
Rush Rehm (1994). Greek Tragic Theatre, p. 58. London: Routledge.
If Classical Greek drama ever had stage directions, our manuscript sources do not preserve them, so when the translation has a stage direction, this is the translator’s guess, based on the dialogue, or just on their sense of how the play should be staged. In the quoted passage from Aias the chorus are repeating an accusation against Aias, that he slew the livestock that had been taken from the Trojans, and it’s possible to imagine staging it so that each chorus member gets to call on Aias in turn.
Dramatic as this idea seems, it is doubtful that this is how Aias was originally performed, because this is the first entrance of the chorus, and the usual practice was for the chorus to sing an ode as they entered, known as a “parodos”. Richard Jebb says of this speech:
134—200 Parodos, in two main parts, viz., (i) 134—171, the anapaestic marching-song, or parodos proper, sung by the Chorus as they enter; (2) 172—200, the lyric ode, sung after they have taken up their position in the orchestra. […]
The Chorus of fifteen Salaminian sailors enter the orchestra from the spectator’s right (as they come from their quarters in the Greek camp). They march in three files (στοίχοι) of five men each. At the close of the anapaests (v. 171), they form themselves in three ranks (ζυγά) of five each, facing the proscenium.
It can scarcely be doubted that the anapaests were chanted by the whole Chorus, and not by the coryphaeus alone.
Richard C. Jebb (1896). The Ajax, p. 31. Cambridge University Press.