I think, once we see the EPA testing results, that the Earth Dreams design is much more efficient than the r18a it replaces. The other things mentioned also contribute a great deal in the resulting MPG. Honda is no slouch when it comes to engineering. I have been impressed that the r18a is more efficient than Chevy's 1.4L turbo motor. Better mileage and lower emmisions, so this new 2.0L NA motor is bound to be better.
As mentioned above, fuel economy numbers don't come entirely from the engine. Note that the 2015 Civic HF gained a 2mpg higher rating simply through lightweight aerodynamic wheels, thinner tires, rear spoiler, underbody panels and slightly lighter weight.
Speaking of which, note too the MPG. 2015 HF R18: 31/41/35 combined. 2016 LX K20: 31/41/35 combined.
Personally I'm not convinced that the R18 is the less efficient engine, but it was at the peak of what can be done with SOHC. The K20's advantage is that it's DOHC which allows more precise valve control with dual VTC, as well as a future upgrade in the form of direct injection.