I believe that this is the old pro-Moscow Comintern Iraqi CP. The CIA supported Saddam in his early years in the Sixties as a "staunch anticommunist", and he repaid the favor by hanging many of their members. Which is of course why they are so happy now.
For this kind of old line Comintern trained organization, this is all "theoretically" justified in terms of a "Popular Front" (with the CPA), in a "democratic revolution against fascism", and so on in an utterly vulgarized form of "marxism". It's a purile logic at the same low level as the "postwar reconstruction" fantasies of the neocons. Oh yes, once again we're in a common front with Uncle Joe in the peoples' war against fascism. Pure HitchThought: Funny, though, isn't it, that Hitch now finds himself in league with the lineal descendents of Joseph Stalin, the ideological blood brothers of the very North Korean regime Hitch also inveighs against.
There are different communist parties in Iraq:
This is the ICP: http://www.iraqcp.org/framse1/index.htm
This is the worker-communist party: http://www.wpiraq.org/english/
LOL, is all I can say. Enjoy the circus.
-Brad