npm install eslint-formatter-stdout

cat $PATH_TO_FILE | eslint --format stdout --stdin --fix-dry-run --stdin-filename $PATH_TO_FILE

No.

cat $PATH_TO_FILE | eslint --format eslint-formatter-stdout --stdin --fix-dry-run --stdin-filename $PATH_TO_FILE

No.

Yeah, but not like you want it to. Why? Who knows. But if you set --format to the fully qualified path of the formatter index.js it works.

cat $PATH_TO_FILE | eslint --format "$PATH_TO_NODE_MODULES/eslint-formatter-stdout/src/index.js" --stdin --fix-dry-run --stdin-filename $PATH_TO_FILE

Why do you have to do something stupid like this? Idk—take it up with eslint. Their docs indicate that it automatically looks in node_modules for packages starting with eslint-formatter-.

Literally every other formatter does that. If you don't have a use for printing the linted code to stdout instead you're in the wrong place.