Results of troubleshooting:
The IntelXDK "Is in IntelXDK" condition is not evaluating as true when I compile to Crosswalk 184.108.40.206 (stable) or to 220.127.116.11 (beta).
The IntelXDK "Launch External Site" action is not firing in either of the beta or stable Crosswalk releases.
The Browser object's "Open in a New Window" action IS firing, but it is not opening a new window. Rather, it is navigating to the new page. But without the back button, you are stuck on the new page and can't go back to the game.
I hate to say it, but I might be forced to use CocoonJS because of this.