Contact customer support to have your account manually removed.
Go to http://help.newegg.com/app/home_iframe/site/CAN#ContactUsTab
Choose “Account / Other” from the tabs on the left.
Click “Other Account Related Questions”.
Click “Submit” and fill out the form – politely ask for the cancelling of your account.
UPDATE: Several users reported that NewEgg does not remove your account, but instead suggests to randomize your personal details. So we’ve put NewEgg on the blacklist for now.