"Why there's no definite article in “The first rule of fight club” before the last noun?"
You mean, why does it not say "The first rule of the fight club...."?
The answer is simple - "Fight Club" is a noun. It is the name of the club.
Let's say for example that there was a swimming club called "Swim Club". You may refer to this either as:
I don't really know if there is such a thing as a fight club, but lets say for example that you took away the word "fight". He could have said:
The first rule of the club is....
But he didn't, because he referred to the club by its name.
You may find this article useful, Dropping the Definite Article. However, please be aware that, as @FumbleFingers has pointed out, there really isn't a set of rules that you can apply in all situations that will tell you when you can drop the definite article. English grammar is peppered with various rules for all sorts of things, and usually they are followed by a list of exceptions to those rules.
To quote Captain Barbossa from 'Pirates of the Caribbean":
[Rules are] more what you'd call "guidelines" than actual rules.
We native speakers usually 'know' the rules from regular usage. When we are speaking, we don't have time to apply lists of rules, so we say what sounds right to us based on what we have heard, said, learnt and internalised over many years. Which explains why we sometimes speak ungrammatically.
If you look at section 2 of the link above, you will see that the definite article is usually left out after proper nouns (except when it isn't). Proper Nouns are the names of persons, places, organisations, etc., and the first letter in each word of that name is spelled with a capital letter. All quotes that I could find on-line show the following:
"The first rule of Fight Club is you don't talk about Fight Club."
Please note that Fight Club starts with capitals. I have not read the book, so I cannot confirm if that is how the author spelled this name. It would appear that the author followed the convention that the definite article is not required before proper nouns.
My take here is a different to the "proper name" one: while the use of a proper name (which would be uppercased) would indeed warrant not using an article, I think that here it's more the use as a domain qualifier which makes this sound better without an article.
That would be comparable to "in heaven" or "in love and war".
You also have sayings like "what happens in $x, stays in $x". This construct makes clear that neither a particular instance of $x nor an unqualified instance of $x are intended, but rather some general domain encompassing all instances of $x.
While this domain-specific drop of an article is most prevalent with "in" (cf "in transit", "in orbit", "in school"), it can be used with other constructs.