Dexos 1 certified oils do not necessarily provide fuel economy benefits over any other equivalent but non-Dexos certified oils. Just be sure you are using the correct type and weight of oil specified in the owner's manual and you will be fine. Lighter oils (weight) can provide measurable fuel economy benefits, but there are downsides to using a weight not specified by the manufacturer.
Basically, Dexos is a certification given to a specific brand/weight of oil if it passes multiple tests. The oil producer must pay a fee to GM for Dexos testing and certification -- this fee pays for the testing costs and also includes a fee to allow the oil producer to use the Dexos logo on the packaging. The Dexos tests are pretty tough, but there are many very good oils out there that will pass the Dexos tests but the producer has chosen not to undergo the certification process. Imagine all the fees if an oil producer chose to test and certify every type and grade of oil they make: 0w20, 5w20, 0w30, 5w30, 10w30, 5w40, 10w40, 5w50, 20w50... then add in synthetic and synthetic blends, high mileage varieties, extended performance oils, etc etc. All these types are often made by a single oil company. Obviously Dexos is a cash grab by GM but it's working for them. All other things being equal, I would pay a couple dollars more for a 5qt jug of oil that has passed the Dexos testing process vs an oil that has not been tested but would probably pass the tests. That's just me.