If you believe this stuff to be an "Actual Explanation" I am extremely disappointed in you. The heroic Shia militias there to save the day from the evil control freaks of Sunni Arabs of Iraq. If this doesn't scream biased I don't know what does.
No idea what part of the articles you don't agree with, it all makes sense to me.
As for Shia groups, the current plan as discussed in Riyadh seems to be strengthening IA forces to eventually go in the direction of repeating 2008, using IA to dissolve forces operating outside of state control and integrate it's remaining fighters but this plan can only be implemented after the ISIS chapter. For some that still is a Safavid army but not as much as the others. Other option is ISIS.