I am laughing... Because I don't know what the icon thing is.
But, in order for site email to be not directed to your spam box or to be picked up by the spam filter, you may need to inform gmail that you are not receiving email from the site. You will need to let them know the email address from the notifications. Maybe try adding this address to your address book, to see if that works.
If not, try changing your registered email address to see if they are received at another email address. Just a few things to try. I know you're laughing now.