Leave syntax alone, I would say data structure is not algorithm, but those two are so mixed.

A clever algorithm usually has one and more clever data structure(s) to support it, or even make it possible. At the same time, a data structure is clever, usually because it can be used in some clever algorithm, and improve it.

Is "for loop" in ASM a type of data structure? Your friend should reconsider his position on this. It migth seems to be data structure from certain perspective, but it is definitely not. Part of the strength of human thinking is the ability to differentiate seemingly similar stuffs from each other.

Data structure is how things are organized, not how they are being handled.