I've collected a few Daruma tea wares and love the image! My avatar is from one of them (the Daruma is on the other side)
A friend told me besides its religious status, Daruma in Japan symbolizes indomitable (because he was the zen patriarch who faced a wall meditating for 9 years) . So the Daruma doll is often in that shape (roly poly?) - as showed in your link. There are traditional toys of similar shape in China, but they don't carry as much spiritual message as Daruma doll. Daruma doll, because of its shape, never fall down. That's also why my Daruma kyusu this proverb (as showed on my avatar) - falling down 7 times and getting up 8 times, that is life!
My friend also told me traditionally Daruma dolls are for making wishes - typically for students who want to get in college, or somebody who wants to start a business, win the love of a woman... You would get it, paint one eye, and keep it. The plan is, when your wish comes true, you would paint the other eye. But he also said there must be many one-eyed Daruma dolls in many people's attics
But anyway, I like the way people pray to a Daruma doll. It's not exactly the same as just asking a god for something. It has the idea that one should learn from Daruma about his unyielding spirit and then there is good chance to succeed.