From the GEnx TCDS:
EXTENDED TWIN ENGINE OPERATIONS (ETOPS)
The GEnx-lB54/1B58/1B64/lB67/1B70 engine models are not ETOPS eligible. They do not meet the requirements of 14 CFR Part 33 amendment 33-21, section 33.201."
And from the Trent 1000 TCDS:
"NOTE 13. These engines are not ETOPS eligible according to provisions in FAR 33.201"
I do know that engine/airframe combinations must be certified for ETOPS. However, the fact that an engine is not "eligible" for ETOPS sounds starnge. Can anyone explain?