The essense of +Vigano's argument against the ecuмenicity of Vatican II is this:
"The convocation of an Ecuмenical Council has as its purpose the solemn convocation of the Bishops of the Church, under the authority of the Roman Pontiff, to define particular aspects of doctrine, morals, liturgy or ecclesiastical discipline. But what each Council defines must in any case fall within the scope of Tradition and cannot in any way contradict the immutable Magisterium, because if it did so it would go against the purpose that legitimizes authority in the Church."
So, two criteria:
1) It must define or settle something (morals, doctrine, discipline);
2) What it defines must fall within the scope of Traddition (Congar said Dignitatis Humanae represented materially the opposite of several provisions of the Syllabus of Pius IX).
Clearly, Vatican II fails these crieria, so how can it pass itself off as an ecuмenical council?
The council is not legitimate, as Vigano explains:
"All this stems from a postulate that almost everyone takes for granted: that Vatican II can claim the authority of an Ecuмenical Council, before which the faithful are supposed to suspend all judgment and humbly bow their heads to the will of Christ, infallibly expressed by the Sacred Pastors, even if in a “pastoral” and not dogmatic form. But this is not the case, because the Sacred Pastors may be being deceived by a colossal conspiracy that has as its purpose the subversive use of a Council."
Therefore, since Vatican II didn't do what ecuмenical councils do (i.e., define or settle something), and moreover, what it did do contradicts Tradition, it represents a colossal illegitimate use of authority contrary to its purpose, and consequently, Vatican II is not an ecuмenical council.