The resistor is added in series with the battery and the LED. In a series circuit, the current is the same in every element.
Thus, lower current in the LED means lower current in the battery, which means less power is being drawn from the batteries, which means longer run times.
You could dim the light by placing a resistor in parallel with the LED. However, this would be phenomenally stupid, as it would increase the load on the battery, making the run time shorter. Nobody clever enough to bring a product to market would be this stupid. I don't say that to insult anyone, but rather to say "NEVER GONNA HAPPEN!"
Now, to go beyond the OP's question: As archimedes points out, there is now power coming from the battery that doesn't go to the LED, but to the resistor instead. This power loss represents a lower efficiency of the system in transferring power from the battery to the LED. The math here is quite clear and unambiguous, given only the information presented.
However, due to the highly non-linear behavior of the LED, this may very well NOT cause a lower efficiency in converting battery power to light. In fact, it may well improve it.
Say your LED draws 100 mA on high power and 50 mA on low, and say that on high it generates about 30 lumens. Because the lumens/mA of LEDs tends to fall with increasing current (and vice versa), at half the current you are likely to get a little more than half the light, so maybe 15.5, maybe 16 lumens. It's not a big effect, but it's quite often real (improvements in lm/W are much larger than in lm/mA).
Since you cut the current in half, your batteries should theoretically last twice as long, and as shown above, you're likely to get more than half the light. Overall, that's improvement in efficacy.
But it gets even better. Because batteries (especially alkalines, and even worse, carbon/zinc) have lower capacity at higher loads (and vice versa), cutting the current in half will give you more than twice the run time, compounding the improvement in efficacy.
Each of these effects does have a point of diminishing returns. But it is typically at least a factor of 10 below the rated current of the LED, and for the battery it's where the run time is starting to be a significant fraction of the shelf life of the battery, so it could be weeks for a NiCad, years for alkaline or lithium primary cells.