> Can you do this without authorization from the game creator?

Yes, of course you can!

> Does this fall under the doctrine of "fair use"?

A more difficult question as there is no hard-and-fast definition in the law of what exactly falls under fair use.  The owner of the rights to the game may have no issues with what you're doing with your Wiki and even decide that it's good for their business.  In some cases these things even get sponsored.

On the other hand they may view it as a threat or unfair competition and claim that it's not fair-use.  In this case you will likely receive a "cease-and-desist" request from their lawyer and then you can choose to either comply or take it to court.

Will you prevail?  Perhaps, it just depends.  Will it cost you money?  Almost certainly and it may be your undoing financially depending on how things go.  Most people doing this sort of thing just shut it down rather than fight.

There are some things you can do to make your project as "safe" as possible.  First of all make sure that it's abundantly clear that you are not associated with the game itself.  Be extremely careful in using their logo, names, descriptions, and anything else they claim as a trademark or copyrighted work.