If the Guitar Hero version feels louder to you, it is because it is more dynamic. It has more variety in the average level, and more contrast between the loud and soft sounds, so it sounds more lively, more energetic and more exciting than the overly crushed CD version. (It doesn't sound as good, in some other ways, though - see "Point Four" in this post.)
How do I know the two are level-matched ? Partly because I've listened to them and can hear they match - balancing levels is a crucial skill for a mastering engineer. But also because measurements back this up, as can be seen in the graphics of the videos.
The two screengrabs here show the same point in the song from the video. look at the level display, highlighted by the red arrows. First look at the Guitar Hero version (GH). The pale blue bit shows the peak level of the music, and the darker blue shows the average level. So we can see that the peak level at this point is almost up to the maximum, whereas the average level is about 10 dB below that. (Click on the image to see a larger version)
Now look at the CD graphics from the same point in the song. The average level is the same - about 10 dB down. But the peak level is barely any higher - about -7 dB or so, instead of right up at the top.
This fact that the average level measurements are equal confirms that the clips are level-matched as I'm claiming. Our ears judge loudness by the average level, NOT the peak level, so they are matched in loudness at the same point in the song.
(Actually it's quite a bit more complicated than that, but this explanation is close enough for the point I want to make in this post. There's more about measuring loudness in this post.)
So why do some people feel the Guitar Hero version is actually louder ?
Try watching the video again, concentrating on the meters. Probably the first thing you'll notice is that both the pale and dark blue meters jump up lower and higher on the GH version, just as the overall graph goes higher and is more spiky. Doesn't this mean it's louder ? No. The dark blue meter is centred around the same point on both versions - roughly 10 dB down from the maximum - so the average level is the same, and over the course of the whole track or album, the ear judges it's level to be the same.
However it feels louder, because it has more highs and lows, more contrast - it's more dynamic. The contrast between the loudest and softest parts of the sound - in this case the drums - is much greater, so it sounds harder and punchier. And crucially because it's overall level hasn't been pushed so hard, it hasn't been over-compressed and crushed, so it doesn't have the ugly distortion of the CD version.
As I've said before, the Guitar Hero version isn't perfect - far from it. In actual fact, it's a bit too dynamic for this style of music - rock requires a "wall of sound" effect, to some degree, and the Guitar Hero version doesn't go far enough in the direction. But the CD is so crushed and so distorted, that out of the two it comes off by far the worst, for me.
As examples of what a great, dynamic rock recording can sound like, check out the Machine Head album "The Blackening" on iTunes or Amazon, or even this BBC live recording of Metallica themselves from last week:
(This one has a bit too much compressor-pumping in my opinion, but still beats the CD by a long shot.)