I'm just testing something that will do pretty much this.
In the developer's forum (click 'forum list' option - it is one of the 'hidden' forums) there was a request for RSS feeds. I have knocked up a prototype, and it works quite nicely.
So using an RSS client, I can view all my public games, and click thought to make my moves. One RSS client ran as a tool bar on IE, which was very nice, but broke when the Goolge tool bar was installed, so I will try to find an alternative. Of course, you can stick this RSS feed into your own website if you wished, then you wouldn’t even need to go anywhere near RHP to check your games.