Do I have to provide the purchasing receipt to service center to get my Early2011 fixed in Repair Extension Program for Video Issues?

Well, Apple states in the warranty that they may request the purchase receipt; I do not know what an authorized service center in Egypt would require. However, the serial number should be available in Apple's records and they could look it up that way - if the seller did not remove it from his support profile, it may still be in his/her name.

It really doesn't matter what other service centers have required from other people - you need to deal with the reseller you are in contact with. In my case, I called Apple (in the US) and they looked up my machine with the serial number. I would tell the service center to check Apple's database, not another reseller's. And, I would contact Apple directly; if you do not have an Apple store in your country, contact them in the US - use the contact us link at the bottom of the page.