A close reading of his resignation letter shows Benedict may have addressed this point.
"I declare that I renounce the ministry of Bishop of Rome, Successor of Saint Peter, entrusted to me by the Cardinals on 19 April 2005, in such a way, that as from 28 February 2013, at 20:00 hours, the See of Rome, the See of Saint Peter, will be vacant and a Conclave to elect the new Supreme Pontiff will have …More
A close reading of his resignation letter shows Benedict may have addressed this point.
"I declare that I renounce the ministry of Bishop of Rome, Successor of Saint Peter, entrusted to me by the Cardinals on 19 April 2005, in such a way, that as from 28 February 2013, at 20:00 hours, the See of Rome, the See of Saint Peter, will be vacant and a Conclave to elect the new Supreme Pontiff will have to be convoked by those whose competence it is."
Benedict's resignation states he resigns "in such a way, that as from 28 February 2013, at 20:00 hours, the See of Rome, the See of Saint Peter, will be vacant..." It seems he's covering his bases. While he did not say he resigns the office of the Pope, he does resign "in such a way" the papacy (he gives its formal titles) "will be vacant" henceforth.
If renouncing the office is, as you suggest, indeed necessary for being a valid pope and Benedict states he resigned the See of Rome "in such a way" it "will be vacant and a Conclave to elect the new Supreme Pontiff", does that not include the office as well?
Benedict's standard for renouncing the ministry is that he does so in whatever manner ("in such a way") that requires electing a new supreme pontiff, whatever that might entail. Surely that includes the office as well, yes? o.O
Personally, I suspect much of the questioning of the validity of Benedict XVI's resignation stems from his successor's obvious radicalism and consequent unpopularity. If Pope Benedict XVI had resigned and the conclave elected Pope "Traditionalist the First", very likely it would be the leftists who would instead be challenging the legitimacy of Benedict's resignation.
GTV canon lawyers would be too busy cheering the new Pope's universal reinstitution of the traditional Latin Mass and unprecedented expulsion of dozens of corrupt cardinals to argue the new Pope was technically invalid and the more docile and retiring Benedict XVI's papacy still valid.
Since that (sadly) isn't the case, they're challenging Francis' woeful papacy with a tacit yet very clear position of "exitus acta probat"
...or so it seems judging by the tenor of the comments on this site.