What could cause “connect ETIMEDOUT” error when the URL is working in browser?

When behind a proxy you need to make the following modifications (as explained in this answer):

• put the proxy host in the host parameter
• put the proxy port in the port parameter
• put the full destination URL in the path parameter :

Which gives:

var options = {
    host: '<PROXY_HOST>',
    port: '<PROXY_PORT>',
    path: 'http://www.boardgamegeek.com/xmlapi/boardgame/1?stats=1',
    method: 'GET',
    headers: {
        Host: 'www.boardgamegeek.com'
    }
}