By Rules as Written: yes, he should have his 6 racial HD o top of his 8 barbarian levels.
The main assumptions behind the design choice described in the Monsters as PCs are:
- Racial HD for playable races are worse than a typical PC class (they could be better than NPC classes such as the Warrior). On the long run this difference widens.
- Racial HD of a monstrous race take the same niche of both the character's race and class. That is: they are a single game element that must take the burden normally spread over 2 game elements.
These are the reasons because CR is considered a better measure for a monster PC effectiveness during adventuring than his mere HD, and why you should usually compensate it by another 50% (up to one half his CR) while the group levels up.
These are the RAW, and you can find out the @AceCalhoon's excellent answer to an analogous question.
But, comparing the resulting character with a 10th level, equally equipped half-orc Barbarian we see that something has gone wrong.
CR is not a good measure of a monster effectiveness as a PC: it is a good measure of how many resources he depletes from a canonical party during a typical encounter. Most monsters aren't designed to stay on the scene for more than one fight: that's the PC's role.
In fact, many monster have really nasty racial features that could tilt the scale a lot. Special forms of movement or defense (like natural armor, being incorporeal or invisible, etc.) should be taken into account when using a weird critter as a PC race.
Dungeons and Dragons 3.0 and 3.5 introduced the concepts of LA (level adjustment) and ECL (effective character level).
Level Adjustment is an amount of "fake" levels that must be added to the race's HD in order to confront it with a base race with levels in PC classes.
Effective Character Level is simply the race's base HD plus its LA.
You can find a list of them on Savage Species (a 3.5 manual on the topic of playable monsters). The list can be found online on the relevant page of the D&D Wiki.
As you can see, a minotaur's ECL is 8th (that is: LA +2). So, the 2nd-level Barbarian in the example is supposed to be in par with the iconic 10th-level half-orc Barbarian. The quick and dirty rules provided with Pathfinder's on this matter are totally out of balance.