RMAA test means nothing to me.  For sound quality, there's a lot of things that "Graph" cannot show.

Etc, soundstage, output power, details...........

Not to undermine your effort. But measuring the Touch under no load (Not plugged earphones) is like measuring a car acceleration without starting the engine.

I'm not into RMAA procedures but a few people around here know the proceedings. I think that you need and y-splitter.

Thank you for taking the time to investigate. You've confirmed something we have all suspected with the fourth generation iPod Touch. I measured the iPhone 4 and the original iPad, and got similar numbers even while driving a load. I have a few questions:

1. With no load, how much stronger is the Discman's output? At maximum volume, what are the numbers in the RMAA level adjustment window?
2. Which earphones did you use as the load? The one that came with the Discman or the iPod? Another model?
3. Were the players still at the maximum volume when you retested with the load?

It's also good to know an amplifier's output impedance so that we can more easily predict how the amp will behave with different headphones. We can estimate the output impedance with additional measurements: How much does each player's output drop when driving the load? You can use the numbers in the RMAA level adjustment window. Just loop the calibration signal or use a different test tone. What's the difference in level between load and no load? Try this with a few headphones and report your findings. With this test, set the players' volume controls at the levels that you would use to listen to music normally. That may be different for each pair of headphones.

1. They're within 5 dB of each other, so the maximum output of the Discman isn't that much hotter. The iPad and iPhone 4 can manage around 950 mVrms. I will guess that your iPod Touch is similar.
2. The original iPod earbud: Use your meter to measure the DC resistance of the earphones. The three conductors on the headphone plug are termed tip, ring, and sleeve. Measure the resistance from tip to sleeve or ring to sleeve. Earbuds usually don't have crazy impedance-vs-frequency graphs, so the the impedance at 1 kHz shouldn't be too far off from the DC resistance. I'm guessing 32 ohms as a ballpark figure.
3. Some sound cards (like the E-mu 1212m) will let you boost the input signal. That will let you take a good measurement in RMAA even with low signal levels from the players. I don't know if your STX will let you do it. Or you could play the test signal while being recorded by Audacity (freeware) or another software recorder, normalize the recording, then let RMAA analyze the resulting file.

But we don't even need to do all of that. We just want to know how much weaker the signal gets after you plug in the earbuds. You can use Audacity to generate a 1000 Hz sine wave. 30 seconds should be long enough for you to take measurements. What does the RMAA level adjustment window say when you're playing that tone? How much does the output drop when you plug in the earbuds in the splitter? We don't need to leave the level adjustment window for this test.

Alternatively, you can use your meter. Set the volume level to the normal listening level for the earbuds. Play the tone, record the voltage. Now plug in the earphones into the splitter. What does the meter read now? Most inexpensive meters aren't as accurate at 1000 Hz as they are at 60 Hz, but don't worry. We're interested only in the relative levels. If you're interested, you could conduct the test also at 60 Hz, just to get another data point.

These measurements will give us a rough idea of how close the player's headphone output is to an ideal voltage amplifier. The headphone amp is like the water supply to your bathroom. How much weaker is the stream from the faucet when you flush the toilet? How much is the output weakened by the additional load?

An ideal voltage amp doesn't change the pressure at all. The Sandisk Sansa Clip+ is a stiff supply--its voltage doesn't get much weaker when you plug in the supplied 16-ohm earbuds. Does the newest iPod Touch exhibit the same grace under pressure? So far, your measurements say that it's getting close.

BTW, if you have a passive inline volume control and a headphone extension cable, there's a quick and dirty way to get a more precise test load than a pair of earbuds.