Please follow the laborious instructions at the deletion link. This (probably) goes for player accounts only. The RS site account may be different. Heck, why not ask at their support address to delete it? That is: firstname.lastname@example.org.
Direct removal link: http://services.runescape.com/m=rswiki/en/Account_deletion
If you signed up for RuneScape using a third-party login such as Facebook or Twitter, you probably want to revoke all access from RuneScape. Click the icon below to find out how.