The chart's correct. It doesn't refer to the EME and EMW NDBs at East Mids, it refers to the I-EME/I-EMW DME installation which is next to the runway and associated with the ILS system.
So on the DTY SIDS chart, I-EME and I-EMW are effectively the same thing - it doesn't matter which end of the runway you're taking off from. Flights don't take off towards the EME or EMW NDBs, rather they take off away from the I-EME/I-EMW, and turn at varying distances from the DME.
LTP