In French, it is very common for predicatives (attribut) to lack articles (Grevisse §586 b), and indeed in this construction, called an attribut du complément d’objet, “cadeau” is a predicative to “cahier”, which is why the article drops.

I’m not sure Circeus’s answer (while valid) is enough to answer your question.
These two sentences are correct:

Regarde le cahier que Than reçoit comme cadeau.
Regarde le cahier que Than reçoit comme un cadeau.

In the first one, the speaker adds the precision that he/she talks about the notebook which was offered as a gift. In the second sentence, Than receives a notebook and a precision is added that it looks like a gift, but maybe it isn’t.

Note: With this simple construction, because the article disappears, French is not able to make the difference beetween “as a gift” and the less common “as the gift”. One would need complex paraphrases to express the latest.

“Comme cadeau” translates as a gift.
“Comme un cadeau” translates as if it were a gift.

Ex: Cette année, sa mère offrit à Marie un ordinateur comme cadeau d’anniversaire. (This year, her mother gave Marie a computer as a birthday gift).

Ex: Marie accepta le manteau comme un cadeau de sa mère. (Marie took the coat as if it were a gift from her mother). (Her mother passed away and her father gave Marie his late wife’s coat).