When a government repeatedly ignores peaceful appeals for positive change, how should the frustration of people be expressed (short of taking up violence)? Fasting is a peaceful method of putting one’s self in jeopardy in order to bring attention of the powers that be.
Even as per the book definition, "blackmail" applies to the use of extortion or threats of causing harm in order to obtain material benefits for self. Anna threatened no one. He demanded nothing for himself.

The government’s agreeing to Anna’s demands was a democratic (not coerced) victory because the tiny fraction of the people of India who participated in the action represented the hearty desires of the masses against corruption. It was the massive outpouring of public support worldwide that caused the government to bow and not just Anna’s fast.
At least here, the government’s action also needs to be commended where they did not make it a prestige issue or try to use brutal force to put down a people’s movement (unlike Egypt and Libya).

Gandhi fasted even after independence. Furthermore, Ambedkar’s statement above was made in the euphoria following independence. If Ambedkar were to see the state of affairs today, he would have advocated all the methods of peaceful civil disobedience, including fasting.
In reality, Gandhi’s fight was not against the white-skinned man (British) but rather against the methods of governance that amounted to injustice, national loot, and falsehood. This is the state of the nation even today, and thus those methods of peaceful protests still hold good.