Its not only compression ratio. Higher octane will allow controlled loop engines to use more timing advance. That is why you do get slightly better gas mileage with premium fuel - but its not enough of a gain to make it worth paying the extra money.High octane fuel does nothing unless the compression ratio of the engine requires it. Running high octane in a low compression engine is actually ungood, since the fuel doesn't burn completely (octane being the resistance of fuel to compressive detonation) and leaves deposits behind. DI/TDI engines are normally high compression enough to need high octane, but not always.
How any of that helps with GDI - I have no clue. I doubt its much difference.