They acknowledge a (very) secular symbol of Christmas (Rudolph) as well as a secular symbol of Hanukkah. It's just that an expectation to be inclusive with these types of things means an explicit acknowledgement of Judaism. And the design they have is pretty cool.
The Dreidel is a secular symbol that happens to be much older than Rudolph; a menorah would have been inappropriate in the same way as an image of Jesus in the manger.
I'm don't think there is a secularly celebrated version of Hannukah. If you have any references for this, please state them.
Christmas is celebrated as both a religious holiday (by large groups of people in the US and UK, which are large markets for Google) as well as a secular one.
Hanukkah is celebrated secularly by the large minority of Jews that are not religious. It's only celebrated and recognized so widely because of its close proximity to Christmas, the most important holiday in the United States, the celebration of commercialism.
Maybe in some parts of the USA. I have a wooden dreidel on my desk. I grew up in an area with a moderately large Jewish population, and have long been interested in their culture and history.
If you're talking about the dreidel, I don't think any other major religion or culture has a christmas-specific object like the dreidel (that is, a toy that you can build yourself out of paper). It's like berating someone for planting a Christmas tree in his garden but not a turban.
This isn't unheard of, but I expected more from Google.