DME can be used in the published missed, but does not have to be. There are other ways to identify the missed approach fix.
The missed approach instructions are:
MISSED APPROACH: Climb to 1500 then climbing
right turn to 3500 on ATL VORTAC R-005 to TROYS
INT/ATL 15 DME and hold.
The missed approach procedure calls for a hold at the TROYS intersection. This can be identified from the intersection of the ATL R-005 and RMG R-115, by 15 DME on the ATL R-005, or by RNAV from a database.
These multiple methods of identification mean that DME is not required. If an RNAV or dual VOR receivers are used, DME is not needed.