I don't think he's advocating oppressed people to turn the other cheek, he's saying that applying the phrase to his actions is a category error.
If you aren't the subject of oppression then it isn't your cheek to turn. Ignoring others' oppression isn't turning the other cheek, it's tacitly endorsing the oppression.
Also it's likely the origin of the "turn the other cheek" thing was specific to the cultural context in which it was purportedly said, not meant to be some universal truth. Proposing the offender use their offhand had symbolic meaning.
But regardless the point is the manifesto-er is debating a Christian in his head, not himself making the argument.