Several articles such as this one and this wikipedia article claim that the custom of the dreidel have nothing to do with Chanukah. Myjewishlearning has the following to say about the custom:
In England and Ireland there is a game called totum or teetotum that is especially popular at Christmastime. In English, this game is first mentioned as “totum” ca. 1500-1520. The name comes from the Latin “totum,” which means “all.” By 1720, the game was called T- totum or teetotum, and by 1801 the four letters already represented four words in English: T = Take all; H = Half; P = Put down; and N = Nothing.
Our Eastern European game of dreidel (including the letters nun, gimmel, hey, shin) is directly based on the German equivalent of the totum game: N = Nichts = nothing; G = Ganz = all; H = Halb = half; and S = Stell ein = put in.... Thus the dreidel game represents an irony of Jewish history. In order to celebrate the holiday of Hanukkah, which celebrates our victory over cultural assimilation, we play the dreidel game, which is an excellent example of cultural assimilation! Of course, there is a world of difference between imitating non-Jewish games and worshiping idols, but the irony remains nonetheless.
Does anyone know of an early source (Rishonim or earlier) for the phrase "Nes Gadol Haya Sham?" Is it all really a "Sham" (pun intended) or is there any chance it was actually used by the Jews since the times of Chanukah? Did it exist off the dreidel? Do we refer to Chanukah as a Nes Gadol anywhere in early sources?