I suspect Orion is very similar if not based on CodeMirror. The ESLint demo uses Orion’s showProblems method, which accepts a ‘problem’ object, supporting: line, start, end, description and severity. The signature corresponds exactly with CodeMirror’s linter helper (from CodeMirror.registerHelper).
Someone on GitHub has actually written a CodeMirror addon that seems to configure ESLint and adds any errors: https://github.com/angelozerr/codemirror-lint-eslint . I can see some integration issues with that code, but it provides a fairly complete connector.
I’ve seen a lot on Codio’s GitHub, but apart from the CodeMirror repository itself (which seems to be relatively vanilla CodeMirror), I can’t find your specific CodeMirror usage, so that seems to be closed-source, or am I missing something?