sendWebsiteRequest_(request) {
    if (goog.object.containsKey(request, 'id') &&
        !goog.object.containsKey(request, 'requestId')) {
      switch (request.call) {
        case 'openCompose':
          chrome.runtime.sendMessage(
              chrome.runtime.id, this.convertOpenComposeRequest_(request));
          break;
      }
    }
  }
Sends the request from the web application to the extension.
@param  {e2e.ext.WebsiteApi.Request} request
@private