I'd say it's definitely a data structure, but one with a canonical string representation. It may not be fundamentally a string, but that representation is critical to how we convey it's meaning to such extent that it's used across languages and browsers as the method of transport.

JSON is conceptually simpler and there's still a lot of quirks between libraries for that already (e.g. null/undefined, integer/decimal representation, and large numbers). XML has more going on to start, and then you get all the different libraries inventing their own abstractions as you said and it picks up a lot of pitfalls. FWIW; I've messed around a lot with configuration languages and it's definitely hard to get right so I understand how this differences accumulate.