I dont know why the Barbarian would get killed a lot more than anyone else; with a 40' move he has a fair amount of mobility. Perhaps it was a RP thing, "Krusk stay in front line until all foes are smashed!"
Tangent: One of my favorite things about our partys half-Orc Barbarian is that he RPs both the bravery and cowardice of his Orc half. When then are going well, he's up in the front lines hacking, slashing and gloating. But if the situation looks anything but rosy he's calling for Healing and he's keeping an eye on his escape route. ;-)
Which is the way Half-Orc Barbarians SHOULD be played

The party in question has 5 members, and I always thought that the CR was "designed" (guesstimated is a better word) for a party of 4. Adding in a fifth character opens up many doors for the party. And their levels are 5,5,5,6,6 but the Centaur is more of a benefit than and hinderance, I would think that alone is worth another level.
Anyway, I expect the party to win. I would expect the party to win if I designed a 7th level barbarian, or bard, or fighter, or rogue, etc. The difference is that I think the monk could also survive this encounter, because when it is really bad he has the mobility to get out of there, everyone else is slow enough to be tracked down and killed. Viola! a recurring villian.
Yep. And yep

But unfortunately, the CR system goes down the drain when:
a) you add or subtract characters from the party, or
b) you try to make a level X character a CR X.
In my experience, there is NO WAY the latter will work. When we try it in our games, whether I DM or not, the NPC has to be at least four, if not five levels above the party to present a credible threat on his own. Unless you count sword swings as "party resources", it never adds up to enough of a challenge. Which is why templates are your friends

The party with whom I tested this most thoroughly included:
Elven Fighter 7/Sorcerer 1/Arcane Archer 4
Human Enchanter 8/Loremaster 4
Half-Orc Barbarian 5/Druid 4 (died a lot in the more extreme "tests"

Elven Bard 6/Fighter 2/Duelist 4
...with a couple of other PCs that came and went for the "extra party member tests".
As a point of interest, the Half-Orc eventually got reincarnated as a boar (IIRC), which he tried adventuring as until his untimely death at the hands (tusks?) of another boar.
