Since a DDE is the sole engineer, they are the de facto chief engineer and would need STCW III/2 (if STCW endorsements are required).
Whether a 3rd AE can serve as DDE is known as an “equivalent.” There is none that allows a 3rd AE to serve as DDE, when the vessel manning requires either a DDE or a Chief Engineer. See 46 CFR Part 15, Subpart I.