This should fall under the anaphoric usage of the demonstrative series1, which is slightly different from the ordinary usage of the こそあど:
Ordinarily, こ～ is used for "nearer to speaker"; そ～ for "nearer to listener"; and あ～ for "removed from both".
But for this discussion, the こ-series is used as if the object being brought to the conversation is visible and present with the speaker. The listener is unable to use これ to refer to the object even though in the ordinary use of the これ, both the speaker and listener are able to. Once both speaker and listener establish that the object is well-known by both of them in the discourse the use of あ～ takes over, and the use of こ～ becomes unacceptable.
The そ-series is used when the speaker perceives that the listener does not know the referent of the demonstrative; the speaker refers to the knowledge/experience that he perceives that the listener is not familiar with.
The あ-series is used when the speaker perceives both himself and listener to know the referent of the demonstrative; the anaphoric demonstrative refers to the shared knowledge or experience between them.
I'll try to fit the case given within the above analysis1.
In this line, その is used ordinarily. その refers to the 焼き鳥屋 that 部長 had mentioned in a previous context.
From this, I would think that the tastiness of the 焼き鳥 is much closer to the 部長 (he was there and had them, 鈴木さん was not), and, therefore that he would use こんなにおいしい, but my textbook says (but doesn't explain why) to use あんなに when talking about one's memories of a past experience.
By using あんなに, the speaker(部長) perceives that the knowledge of the extent of tastiness is shared (even though it may not necessarily be so).
I think the 部長 is referring to a shared maximum point; that what one human thinks is a great extent of tastiness is not too different from another human, therefore the use of あんなに is reasonable.
(This is not too unreasonable a perception. If you allow me to reverse the polarity, I think if something is "that disgusting" then there would be a reasonably large majority that would agree on the extent of disgust. So if something was "that delicious", it tends to conjure a maximum deliciousness image)
そんなに is used ordinarily, and refers to the 部長's last comment; the extent of how the 焼き鳥 was delicious. The usage of そんなに is not different from the use of その in その店. It refers to something last said by the other person.
1 Chapter 24 of The Structure of the Japanese Language, Susumu Kuno.