I managed to get a little further by not using my beta bookmark.
Went to the main page, then the “Open Beta Update” news item and followed the link in there.
Then I got:
Error_game_webgl – Your browser or device doesn’t support WebGL.
RuneScape uses WebGL to display its 3D world, but unfortunately it looks like your web browser or device doesn’t support it.
There are a few simple solutions to this problem:
1. If you’re not already using a compatible browser, you can download an updated one. We recommend the latest version of Google’s Chrome browser.
2. If you are sure you are using a compatible browser, try closing it and opening it again (particularly if you have a yellow bar telling you that “WebGL hit a snag”;)
3. Update your device’s graphics drivers – if you are using Chrome already and it does not work after restarting, this is almost certainly the cause of the problem. Old graphics drivers are frequently ‘blacklisted’ due to security concerns.
4. If you have Java installed, use our Java web client instead of the HTML5 one.
5. Install our downloadable Java client.
If problems persist, please refer to the Technical FAQs, which can be found in the Customer Support section of our website.
This occurs to me also.
I can however play the HTML5 NIS Beta. but of course that means my game progress is not preserved. Much as I like the new interface and look of the game, I’m not going to use the HTML5 client unless I can actually continue with my game