Stopover in the fare rule refers to the ability to break your journey in DXB for >24 hours (so technically the stop in DXB is an actual stop, not just a transit point - a technicality for the purposes of misconnecting etc.). Many restricted fares on other carriers do not allow a stop in the intermediate point, but EK tend to allow free stops in DXB in the middle of the journey.

It doesn't refer to a stopover that's paid for by EK - as in, they won't cover any costs of taking advantage of the stopover rights, like they would if say, the fare was eligible for Dubai Connect.