That's interesting, unfortunately I don't have an iOS device to hand to check with my game center account.
Could I ask that you submit a ticket via https://support.runescape.com/hc/en-gb/articles/360001552065-Can-t-log-in-? (Click 'no', and then 'no' again, then 'maybe we can help').
Give them the support team the in-game name of your account, explain that you're trying to add a login email to your game center account, and explain that you tried following the guide I linked you to.
Sorry I can't help further at this moment, but the support team should see you right.