You are looking at how China's economy functions today in a few cities, and not how it functions in the vast majority of the rest of the country. More importantly, while China has mostly or entirely gotten rid of the planned economy, it's success has come in large part because of massive monetary interference by the state in the economy, protectionism, forcing western companies to give up some of their IP to do business there, and of course a good dose of slave labor, like every successful economy in history unfortunately (I am absolutely opposed to this last one, and it is one of the things we have profited most from in Chinas's growth).
Countries that moved from a planned economy to capitalism under the IMF and WB's guidance have generally rushed to privatize their industry, have accepted and dutifully implemented all international IP treaties, have opened up their arms to foreign investors and sold their industries to them, and are almost all in much worse situations than China, with no hope of regaining the lost ground for now.
For India, I will only say one thing - India would not have been an IT powerhouse if it had been under colonial rule. The British wanted cotton and spices and other raw or lightly processed materials from India, and that is what it would have been forced to do - same as the path the American colonies rebelled against. Industrializationa and high-technology was for the mother land, not the colonies, in the horrible economic principle of the 'competitive advantage'.
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Related to poverty, you're right, I probably should have given a definition. Extreme poverty means not having access to one or more of the the basic necessities of life - water, enough food not be malnourished, enough shelter not to die of hypothermia or heat, and access to medical care to survive the most common diseases in your region. If you have only these basic necessities and nothing else, you are still poor, but not living in extreme poverty.
From what I understand, the monetary threshold for these should be somewhere around 15 dollars per day to get out of extreme poverty (note that this 'income' includes begging, access to communal resources etc). There are of course many opinions on this number. However, the 1.9 USD value is pitifully low, and you can easily check that yourself: please think about what you can buy for 3 USD in you region each day, without any kind of borrowing, begging, living off the land, sharing etc (as those are already included in the number). Would you consider yourself to not be in extreme poverty?
Note that if we look at malnourishent, the percentage and number of people who are malnourished has stayed roughly the same since we started collecting data (1981), after increasing steadily up to ~2000.
And about people living off the land, they are indeed included in the data since 1981, but not in the data since 1800, as often presented.
Edit: and yes, you are right that people living off the land were usually doomed if they got significantly sick. But this is also true of, for example, everyone living on minimum wage in the US today, so I fail to see what's improved.