Regarde le cahier que Than reçoit comme cadeau de sa copine.
I was wondering why there isn't an 'un' before the 'cadeau'.
I'm not sure Circeus answer (while valid) is enough to answer your question. These two sentences are correct:
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.
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.