It could be a number of things.
No matter what the cause the noise is simply that, noise. It is possible that the DAC inside the M-STAGE is introducing noise into the signal path by having a poor noise floor or high harmonic distortion.
You seem to be comparing apples to oranges here so I need some information. When you listen to the same YouTube video without using the M-STAGE do you hear the noise? If so it could simply be the quality of the YouTube video(s) and the noise is in the signal to begin with.
You could be saturating the DAC/Amp which may introduce a bunch of noise. Try reducing the volume on your computer to say 75%. That way the signal will not have a chance to saturate inside the M-STAGE. Now use the M-STAGE to control the volume.
All I see on their site is the M-STAGE amp. They call their DAC the Matrix Cube and mini. Is it possible that your M-STAGE is really the amp and not the DAC? This would explain the noise due to simple amplification of an already poor signal. Without using a better DAC, because you are using the one inside your Mac, the amp simply amplifies the already noisy signal.
Would you be able to post either a picture of your M-STAGE or a link to the exact picture of what you have? This we can better help you. It sounds like you are amplifying an already poor signal to me. If I remember right the MacBook has a decent DAC in it, but when you connect your amp via USB you may be picking up some serious noise from other components within your computer like the power cord, processor, and mouse if you are using one.
Which of the following is your device:
A) http://www.matrixelectronics.net/matrix-cube-24-192-asrc-dac-headphone-amp-p-186.html
B) http://www.matrixelectronics.net/matrix-m-stage-c-67.html
Here are the listed features for the M-Stage straight from their site.
Features
· New 2012 version with upgraded power transformer and redesigned circuit
· Powerful output that can drive high impedance headphones (up to 600 Ω)
· High quality components including ALPS VR, Nichicon caps, OPA2134 Op-Amps, etc
· 2 sets of line inputs selectable on the front panel
· Can be used as a pre-amp with the line output on the back panel
· Gain selectors can set 0, 10, 18 and 20 dB gains
· Solid build with aluminum faceplate and steel case
· Fully dynamic and well balanced sound on a dead quiet background
Here is another Head-fi member's take on the issue. It looks like they hear the hum at very high volumes too. Perhaps the simplest of solutions is to turn the volume down.
http://www.head-fi.org/t/475618/matrix-m-stage-amp-review-simple-cheap-and-excellent