Why is it called an “Indian file”?

Solution 1:

Presumably because this is the way the settlers thought American Indians walked on trails through the forest. They probably did; if you have narrow trails, this is the only comfortable way to walk them. By the way, in my experience, it's not "an Indian file"; unlike "single file", "Indian file" is not used as a noun.

They walked Indian file.
or ... arranged Indian file.

but not

*They formed an Indian file.

Solution 2:

Indians in single file:

Canadians in single file:

Solution 3:

Just as a point of information, I've lived all my life in the USA, most of it in Oklahoma where (American) Indian peoples are more than 10% of the population and culturally very prominent. To my knowledge I have never before heard that term.

If I had to hazard a guess, this probably relates to the way some particular tribe used to wage war. A lot of tribes looked at warfare as a very stylized affair, much like Europeans did in the Middle Ages. You'd typically get more glory by running up and slapping one of the enemy than by actually killing them (as this was actually more difficult). However, Indians were/are not one people with one coherent culture, so these things can vary quite a bit.

So the term is probably a regionalism.