A small pan on an oversized burner wastes a lot of heat. Some more may be coupled into the pan but much will go into the room (so not wasted completely). It might damage the handle, especially with something low like a frying pan, as this heat is mainly radiated (the glass is meant to absorb very little). The inner burner may be so much weaker than the outer that even a fraction of the power of the outer is a significant increase compared to just the inner. I seem to recall using one with a 600W inner and 1200W outer - if even 1/4 of the power of the outer went into the pot it would be 50% more heat. The specs for yours don't go into quite enough detail but it looks like the inner might be 1200W and the outer 1800W, so not as marked as my example but it still makes a difference. As the heat is radiant, some heat will enter the sides of the pan, contributing to faster, if not very efficient, heating.
But when you say "cook quicker", how are you measuring cookedness? Is this a rate of reduction in volume (which would scale with power absorbed to a good approximation)? Or is it a subjective done-ness (which has more to do with time-at-temperature, so quite strongly affected by how quickly it reaches temperature). Coming to the boil quicker means you could use both until it boils then simmer using the inner ring only (assuming it's not finished when it first comes to the boil). This is likely to be more marked if you're starting from cold, as the additional power of the outer will cover some of the losses involved in warming up the surrounding parts of the stove.