Premise is that longer motor run-time pulls less total power than maintaining higher heat. That may apply moreso to an electric dryer than a gas unit but I suppose the Eco option is included on the gas units for consistency of model features, or for marketing purposes if nothing else. You may come out better on total energy usage (gas + electric) by not using Eco.

I have an older model (last generation) Electrolux and I believe the Eco option also lowers the heat output as it progresses to the dryness level.

Turning the drum hardly uses much power as compared to heating the air going into it.

The only way to actually know would be to calculate how many btus are used in both cycles. Something tells me with gas that the eco option is more about doing less heat damage to your clothes than saving fuel.

saving fuel usually means changing technology to one that is more efficient. That means a heat pump if your already using gas.