I knew nothing about these re-enactments, however it’s clear from looking at and reading the descriptions of the lithographs on his site that re-enactors have huge respect for Indian culture and for history as well.
I found the description of ‘War Dance’ fascinating:
Throughout the French and Indian War, English authorities negotiated with the Native Americans for their military assistance. While not as successful in this as their French counterparts, the English did enjoy some success, due partly to the presence of the Scottish Highlanders, whom the Indians viewed as being similar to them.
Both cultures were tremendous warriors and lovers of a battle, both had great respect for the orator and Chieftain, and both clan and tribe held tightly to their ancient traditions. Their similarities in temperament and philosophy sometimes led the English to refer to the Scots as "cousins to the Indian."
Preparing for battle had its own Highland custom – the Sword Dance. Here Robert Griffing shows a soldier of the 42nd Highland Regiment within the walls of Fort Ticonderoga seeking a prophecy by engaging in an ancient Highland tradition.