Have you tried simply entering your username as the 'email address' even though it isn't one?
Or is there a "log in with username" option to click?
If it is not as simple as this then I am not sure what the way to do this is while keeping a traditional account, but if you are willing to set up a Jagex Account (note that this is the new thing that they are pushing, not the Runescape account that you have had for years), I think you just need to log in to the Runescape account settings page on the Runescape website, click the "Upgrade" button and then use whatever email address you like - it doesn't need to already be associated with your Runescape account.
See the news post "Jagex Accounts - Open Beta Begins!" for more information - I think you'll now need to click "Show more" on the news page to find it.
07-Jun-2023 13:06:08