Ok, look, if Singapore is a Chinese country, than Quebec is a French country, and the USA is a Hispanic one.
I can see where you're going, but I don't think these immigrants make Singapore "Chinese", it makes it a country of Chinese immigrants at most. Ask a third-generation Singaporean if he's Chinese and watch him laugh in your face.
Taiwan's a little different, there are still lots of Taiwanese who would consider themselves "Chinese", but just as many who consider themselves distinct Taiwanese. However, since Taiwan is still politically a part of China, it doesn't really apply as I see it.