How did Christianity change this culture?

Christianity did not change the Sawi culture at all. Christianity was Don Richardson's views on religion therefore meaning it was based on God

and the sacrifice He made by sending His only son to be sacrificed for us. Sinners. That is what Christianity is, but that religion is not what changed the Sawi culture. God changed the Sawi culture.

When you ask "how" did God change this culture we can look at physical aspects of change in the Sawi and of course their Spiritual change as well. Physically, the Sawi were barbaric cannibals that held treachery and betrayal as the highest and most honored act that could be done in their tribe. They wore loin cloths and skulls. They usually had multiple wives. They could only trust their families and no one else, and had a custom of giving a peace child between tribes to hopefully have the other tribe accept and have peace between the tribes, but only as long as that child was alive. The Sawi went from being this tribe, to hearing of the sacrifice given by God Himself, and changing completely. Making clothes for themselves, not practicing cannibalism anymore. They built a church for all tribes to come together and trust each other and worship God as brothers and sisters in Christ, and they started to learn the will and ways that the Lord wants them to live by and change different parts of their individual and personal lives that weren't reflecting God's amazing love through them.

Spiritually the Sawi went from having almost no morals in life at all and having their entire beings revolving around betrayal and distrust and uncertainty. To knowing a little sliver of the pain that God was feeling when He gave His son Jesus to die on the cross, and realizing that He is all that should matter in their lives and wanting and being hungry to learn of Christ and everything that He did and is wanting them to do right now. They went from being scared to eat over at one another's house because of the chance of a treachery and murder, to loving one another and forgiving unthinkable things that were done in the past and moving on to worship the one who gave the ultimate sacrifice for them. That is how God changed the culture of the Sawi people.