I'm the author.
I tend to regard the KML presentation as a legacy app, and if your browser has decent JavaScript performance to use the custom map
here.
As noted in the help section, the KML rendering is at the mercy of the performance of Google's servers, and of late the performance has been variable (including response to selection events in the tree view) - I've left it running to support older browsers.
I'm planning some tweaks to the custom map to make it more iPad amenable. To get rid of the warning dialog add ?nosplash=y at the end of the URL.
If you want a map plotted directly from your briefing on the AIS website, a Google Chrome Extension is
available