They could not help being "moved" by the sight of him. "moved" means emotionally affected; normally it implies sympathy, compassion, humanity, etc.. "after their fashion" means that they were "moved" in a way special or peculiar to themselves, which in this case caused them to beat him, as you say.
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GPYSo, the passage plays on the fact that the interpretation of "moved" relevant to them is different from the normal or expected meaning, and uses this contrast to shed light on their characters.That's why I had question.
vsureshSo moved here can mean that they anger was roused. Am I right?Yes. However, when you first read "moved" that is (intentionally) not what you think of.
GPYHowever, when you first read "moved" that is (intentionally) not what you think of.Yes,I thought they turned sad seeing their boy in miserable condition.
vsureshYes,I thought they turned sad seeing their boy in miserable condition.Actually this "..they gave him a brisk cuffing and sent him to bed" made me think it on that line differently.In that case, you read it exactly correctly.