Its quite tricky because not many are aware of this procedure. I did struggle a bit, but finally found out what to do.
Go to the Immigration Office in Gharafa, building no 1. Take a token (when I went abt 4 months back,the person issuing the token did not have any knowledge about renewal of E-Gate at Immigration office & hence first refused to give me a token. But then after convincing him, he issued a token.) Get to the counter & give him/her your ID/E-Gate card & tell him that you wish to renew it. They are generally aware of the procedure & you should not have any problem.
Pay the required amount by Credit / Debit / ATM Card. The only issue is that you have to note down as to when your E-Gate will expire as this will be different from your ID expiry date.
All the best ...