No, I don't believe you could argue C is purely functional by framing memory as the output of the function because C doesn't treat it as such. Memory in C can be changed even if it is not listed in the inputs or outputs of the function.

He's not really stretching the definition, that's just the lens through which FP looks at the world.

Of course there is state. FP doesn't prohibit state, it just makes it explicit and referentially transparent. But this is in the semantics, not the execution model of the program.