'I would get him'

When George Washington’s father had found an apple tree cut down
in his orchard, he got very angry, and had said to himself,
‘I would get him’, it was said. What does ‘get’ mean’?

On the face of it, ot appears to mean “I would catch up with thim and punish him”.

Usually this expression finishes off with something like ‘for that’ to indicate the reason for wanting retribution as in: Just you wait, I’ll get you for that.