Gandhi's legacy is indeed more for non-violent protest and its methods than for actual Indian independence. But he did shroud the language of independence in Hindu mythology, and he's largely responsible for turning Indian nationalism into Hindu nationalism. This is why he plays a big role in modern Indian history (as opposed to modern Pakistani history).

If Gandhi had not been involved in India at all, it's debatable whether the INC would have adopted nonviolent resistance or gone for more violent methods. But the goal of independence from the British was largely established before Gandhi arrived in India, particularly through the work of Bal Gangadhar Tilak; and the real driving force of the independence movement was the INC, particularly under Jawaharlal Nehru. They adopted Gandhi's ideas, yes, but they adopted the ideas of others as well. For instance, Subhas Chandras Bose was a very influential member of the INC before WW2; he was basically Nehru's right hand man. Yet Bose believed in armed insurrection over nonviolent protest.

And to examine Indian independence from the other side, the British angle, decolonization was a major goal post-WW2. The British simply lost the means to enforce a territory as large as India while gaining little from it.

So again, Gandhi was less influential in British independence than in the establishing of a modern Hindu state. By 1937, it was clear that British India was going to become independent, the problem was the creation of a state that Muslims and Hindus could both partake in without significant complaint.

That said, the person the OP is quoting isn't saying that Gandhi is "ineffective". He indeed says that Gandhi gave the British a hard time. He's just saying that Indian independence would have been possible without Gandhi, and I believe in that assertion. That independence would probably look very different, however.