Sure it does, but the way that LM317 works is that it is only interested in keeping the 1.25V between the two pins. The maximum voltage it can output is 2-3V below the input voltage. Whether you get that isn't guaranteed (unless you change the circuit), but as long as the regulator's output voltage is above the threshold voltage needed to cause the laser diode to pass current, that's all that matters. If you want the input-output margin to be less (for example to use a lower input voltage), you'll have to find a different regulator.
That's the thing with electrical circuits that is hard to grasp at first: only go by what you know beforehand and work your way back to other parameters, not what you think you know or expect. This is especially true for semi-conductors, as they're designed to do "weird" (i.e. non-linear) things not generally possible in passive circuits. For example, you expected the voltage to be constant for the regulator, but that's not what the regulator does unless you set it up to be that way. The only thing the LM317 really does is keep that 1.25V between those two pins, and the maximum voltage it can provide is 2-3V or so below the input voltage. That's it. If you want a specific voltage, you can rig it up to do that, but then the current it would provide might not be what you expect too. There are some interesting circuits in the datasheet, which show other applications and circuit topologies.
