Also, all the docuмents in Vatican II were officially promulgated, and an extraordinary definition is not required from a Catholic General Council in order to require adherence. Anything declared or delivered (see the Tridentine Creed) must be also considered infallible (just in case you try to use that excuse).
You are right, an extraordinary definition is not required to bind us, but the truth is - it is the truth that binds us, decreed through the Church, often via the pope or council. Religious liberty is false, it is a lie of liberals which can never bind anyone - regardless of the method. It is the truth that binds us, not the method.
Also, Pope Pius IX at V1 decreed the necessary criteria for infallibility, if those criteria are not present, then there is no infallibility - "Anything declared or delivered [from a council?]" is not found anywhere among those criteria.