It's not that simple. 'Amped' or 'amplified' doesn't simply mean 'multiplied' - there's a part of a headphone amplifier called a 'preamp' stage. Depending on a circuit, this can either be very complex or as simple as just the potentiometer, either way the basic function of a preamp is to control how loud it goes. I can't remember the more technical part of this, but I think it actually controls (reduce) the voltage of the incoming (input) signal. A typical speaker system for example would have a preamp and a poweramp, and when these are integrated into a single box (but can be designed with separate power supplies), it's called an integrated amp. This is typically what headphone amplifiers are.
On playback devices, let's contrast a conventional HiFi or professional CDPlayer and a typical portable player. A CDPlayer might have dual DACs (one for each channel), an opamp/HDAM or tube output analog stage with a 2volt standard signal, and maybe a headphone amplifier stage with a tube or chip and the supporting circuit driving a headphone. The S:Flo is basically a miniaturized version of all this. Your typical portable player would have most if not all of these integrated into a single audio processing chip. Where the S:Flo would have two Wolfson WM8740, opamps in the analog stage after that for the lineout or into a Philips TDA1308 headphone driver, a Samsung or Cowon would have a single Wolfson WM8994.
Depending on the capabilities of a given audio processor and the circuit design, some players might still have some functions handled by another component after the integrated audio chip, in which case a 'bypass' lineout basically means you skip the potentiometer for the headphone out. Where the audio processor basically handles everything audio related, it either bypasses the preamp circuit in the chip, or if it uses fully digital preamplification*, simply shuts off any control over the volume. In some cases the thing with these do-it-all audio chips is they have a DAC and a headphone amp, but usually nothing like an opamp/HDAM in them (why would a manufacturer assume the typical user would have a headphone amp that needs a lineout?), so the "lineout" is basically just that - "full volume" in the sense that the digital preamp is off and you get the signal from the DAC at its max setting. In some cases the chip was either designed with this in mind or simply had clean enough output; my Cowon S9 and Galaxy S are good used this way with amps. In other cases, well, no; I hated the noisy and tinny analog "lineout" of my iPod Touch.
So basically, you are right that "unamped" in a sense is volume from the DAC, but there's a reason why full-size players have an opamp/HDAM or tube analog stage past the DAC, and not just the DAC directly soldered into the output jacks; and yet neither does "amped" have to be "louder" per se, but simply that a 2V low-level signal would have to be made into, say, high-level signal measured in Watts (or fractions of it, mW, for headphones).
*and not just digital control, but there is an actual preamp circuit somewhere in or out of the audio chip
