Containerized Node server inaccessible with server.listen(port, ‘127.0.0.1’)

Your ports are being exposed correctly but your server is listening to connections on 127.0.0.1 inside your container:

http.createServer(function (req, res) {
    res.writeHead(200, {'Content-Type': 'text/plain'});
    res.end('Hello World\n'+new Date);
}).listen(1337, '127.0.0.1');

You need to run your server like this:

http.createServer(function (req, res) {
    res.writeHead(200, {'Content-Type': 'text/plain'});
    res.end('Hello World\n'+new Date);
}).listen(1337, '0.0.0.0');

Note the 0.0.0.0 instead of 127.0.0.1.