Sorry in advance for the mild thread necromancy:
I take their ststement to mean higher output for entire optical systems or luminaires that use the XP-G2 chip. Since the XP-L HI chip has higher surface brightness it may end up with more total throughput through the secondary optics. That statement implies that the distance between the mounting surface and the apparent location of the die image is the the same for both the XP-G2 and the XL-L HI, so that the parts could be substituted without needing to reposition any secondary optics.
I can't confirm if that's actaully true.
Yes. the main reason flat LEDs like this are advantageous is that they have high surface brightness (or radiance).
LED domes improve overall efficiency and lumen by allowing rays that would otherwise totally internally reflect to escape, but the consequence is they magnify the apparent size of the die by 1.5X, meaning an apparent area of the die by 1.5^2, or 2.25. (it's actually even worse when you consider the image of teh die is distorted when viewed at large angle).
The lack of a dome also means you can place optics such as aspheric lenses much closer. With a dome you are limited to optics that have a long enough working distance (distance from the back surface of teh lens to the apparent location of the LED die) to clear the thickness of the dome.
It also means that components such as light pipes or homogenizing rods can be placed in flush contact with the LED. A domed LED cannot be easily used with devices like
tapered light pipe rods without excessive losses. A combination of a domeless LED, a tapered light pipe, and an aspheric lens can basically be used to form an extremely uniform and high intensity light source suitable for microscope illumination. That's a lot harder to pull off with domed LEDs.