All that webpage does is say if the iphone is covered by a warranty, it does not state who is the person covered by the warranty and in this case it would be his uncle because at the point of sale, the iphone serial number would be registered against the person who bought the iphone, that being his uncle. Therefore is anything was to go wrong with the iphone, Apple would look up the serial numbers and see that it is assigned to his uncle. Transfer of ownership can occur BUT you need the sales receipt for that.
Apple may go out of it's way to help you if the iphone had problems BUT legally Apple are under no obligation to deal with you because you was not the one who purchased the iphone. Let me put it this way, your iphone develops a problem, you ring apple support, they ask you for your name and the serial number of the iphone, they go to check their computer system and notice the iphone has been registered against the name of the purchaser. You tell them that your uncle bought the iphone for you. Support then ask you for more confirmation details, details which would be on the sales receipt. No receipt, Apple turn round and say 'sorry, we cannot help you, get your uncle to contact us'.