The article is specifically about purchasing homes. Even the USA, it also is cheaper to rent than to buy. Buying a home in Singapore has a 6 year waiting list to access public housing with properties exceeding $1m SGD.
Taxes, Transportation and food costs are cheap, but property is not.
Singapore is not really typical of anything anywhere, it's a small island nation with insane population pressure with regards to housing.
Almost any other Asian city from Bangkok to Ha Noi has room to expand. In fact speaking of Bangkok buying a condo there is widely considered a bad investment because there is so much supply.
Beijing has cheap rent, at least for foreigners making western wages. That 10k RMB/month 1 bedroom is supposed to cost 7 million RMB to buy, so you are still screwed if you are looking not to rent for some reason.
I hear Shanghai is much worse, but never lived there before.
Hong Kong has all sorts of crazy building restrictions and is a different story