The rules state that when a warlord is bloodied it retreats exhausted to its controller's HQ, is this "forced" retreat meant to be treated the same as if the warlord had retreated as a combat action, thus passing control back to the player that had just attacked?

No I don't think so, the warlord retreat is a special action where you are giving up a combat turn to ensure their safety whereas being beaten unconscious and sent home is already enough of a downside without additionally losing out on an attack.

When the warlord is bloodied, you do not "spend" a combat turn, change the order of actions, or anything like that. After all, it is possible for a warlord to be bloodied outside of battle (say, by direct damage), right?

The warlord going to HQ when it is bloodied is more like having to put a unit in the discard pile when it is destroyed than anything else. It is just a result of the action that bloodies it, not a separate action in and of itself.