You pointed out that his legitimacy was challenged, but you have yet to detail the constitutionally defined (that is to say legitimate) actions taken to strip him of his title.
You seem to be missing the point. The CoD did not strip Allende of his title, nor did Pinochet. The CoD called upon the military to intervene against Allende's violation of the Constitution and take him into custody. The formal ejection of Allende from office would have certainly followed after his intended arrest by the military on 9/11/73, in which case I believe the constitutional process was some sort of legislative trial that was to take place.
But it never got to that because Allende chose to commit suicide before he could be transferred into military custody.