***** NOT A TEACHER *****
Good morning, jasmin.
(1) I have been thinking about this all day, and I can't find an authoritative answer in my books.
(2) So -- although I may be all wrong -- I am going to say that the second "not" IS correct.
(3) Here is my reasoning, which some people may label as lack of reasoning.
(4) Guys would not be smiling after losing a game.
(a) the prepositional phrase ("after losing a game") modifies the verb ("would be smiling") ("not" = adverb). Good sentence.
(5) After losing a game, guys would not be smiling.
(a) Same reasoning. Good sentence.
(6) Guys would not be smiling, especially after losing a game.
(a) I submit this is not grammatical.
(i) With the introduction of a comma and the word "especially," we now have a so-called parenthetical remark.
(a) As I understand it, a parenthetical remark has no grammatical connection with the main clause.
(i) If that is true, then what does "after losing a game" modify?
(a) I submit that it modifies the understood verb in the parenthetical remark.
(i) I submit that the "full" parenthetical remark is:
(Guys) (would) especially not (be) (smiling) after losing a game.
(6) I submit that "Guys would not be smiling, especially not after losing a game" is a shortened version of:
Guys would not be smiling. + They would especially not be smiling after losing a game.
*****
TOM: What's wrong?
GEORGE: I do NOT like you anymore.
TOM: Why not?
GEORGE: (I) ESPECIALLY (do) NOT (like) (you) after telling me that big lie yesterday.
(I do not like you anymore, especially not after telling me that big lie yesterday.)
Good evening! I too have been considering this for many hours. It is not often that I would challenge the thinking of the much admired Parser.
In this case, however, I must disagree. I wish I could explain my reasons in an elegant or at least moderately effective way, but, alas, I cannot.
Here, however, are two reasons. They barely convince even me, but here goes my best, however feeble, effort.
The first reason may simply be a matter of style, but I must say that I fully grasp the meaning from the very beginning when I read, "Guys would not be smiling, especially after losing a game." There is no question in my mind what is meant, and my eye gracefully scans the sentence. Add the second "not," however, and my thought process kicks in. "Wait a minute," it tells me, "what exactly is the meaning here?" I believe I understand, but I am left vaguely troubled.
The second reason is slightly less subjective, and actually touches on grammar, if not logic.
As you point out, the sentence when rearranged is unquestionably grammatical: "After losing a game, guys would not be smiling." If we now add "especially," we get, "Especially after losing a game, guys would not be smiling." This is not a particularly elegant way to say it, but it does work and the meaning is clear. Would we not agree, however, that the addition of "not" would only add a note of confusion? I hesitate to write the resulting sentence, since it offends my sense of grammar, such as it is.
But here it is: "Especially not after losing a game, guys would not be smiling." No, my dear Parser, I cannot accept this. And, as I see it, the second "not" does not somehow become acceptable when we rearrange the sentence.
I'm afraid that I will have to stick with the old adage (OK, I just made it up): two nots do not make a right. At least, they don't when it comes to English.
I put this forward in the spirit of the our guide, the noble lady Grammatica, who inspires us from the Royal Portal of Chartres.* May she inspire one of our correspondents in ESL land to shed light on this troubling issue.
My best wishes for a lovely and grammatical weekend.
*
Marginalia -- The Journal of the Medieval Reading Group at Cambridge