Is "it is a fun game" correct?

“It is a lot of fun,” sounds correct, but not, “it is a fun game.”
Isn’t fun a noun? Then why is it used as an adjective?
I have heard this usage even by literary giants, so this cannot be a common mistake.
Should “funny” be used in stead?

EDIT
Moral of the story: Fun has become an adjective colloquially, hence it is impossible to see it as wrong.