Although Mahatama Gandhi was not the originator of the principle of non-violence, he was the first to apply it in the political field on a huge scale. The concept of nonviolence (ahimsa) and nonresistance has a long history in Indian religious thought and has had many revivals in Hindu, Buddhist, Jain, Jewish and Christian contexts. Gandhi explains his philosophy and way of life in his autobiography The Story of My Experiments with Truth. He was quoted as saying:
"When I despair, I remember that all through history the way of truth and love has always won. There have been tyrants and murderers and for a time they seem invincible, but in the end, they always fall—think of it, always."
"What difference does it make to the dead, the orphans, and the homeless, whether the mad destruction is wrought under the name of totalitarianism or the holy name of liberty and democracy?"
"An eye for an eye makes the whole world blind."
"There are many causes that I am prepared to die for but no causes that I am prepared to kill for."
No, Gandhi is relevant here because his values stand in contrast to the dominant Western values the colonialist powers imposed on the world.
Although America called its indigenous population "savages," "killers," and "scalpers," many Indians sought nonviolent means of accommodation. They sued for peace, signed treaties, resisted passively, fled, or stayed in place and did nothing.
It would've been interesting if the Ghost Dance movement of the late 19th century turned into a full-fledged campaign of civil disobedience. It might not have worked, but violent reprisals didn't work either. Geronimo and his guerrilla band ended up in the same prison camp as the Apaches who settled into farming on reservations.
For more on the subject, see Winning Through Nonviolence.