[I]t was in fact a popular game in Europe, and especially Germany, in the 16th century -- particularly around Christmas time (aha!). As this site explains, the word 'dreidl' itself is derived from the German word drehen, which means to spin...Read the rest here. And while we're at it, check out the post last year on the real reason for Chanuccah: it's connected to Sukkot.
So far, so unsurprising. I was intrigued to discover, however, that not only is the game itself Germanic in origin, but that the letters on the dreidl come directly from the German as well.