JSON is great, but the thing that bugs me about this usage is that it is essentially a bloated version of a "normal log". You don't need the field names, braces, :, quotes or in-fact most of the characters there, just single character delimited columns (traditionally comma, space or tab) with rows delimted by some other character (traditionally newline), some rules for escaping (or not) and the first row as the field names (if they are not obvious). Its more human readable, more machine readable and shorter than JSON - and actually, its already the unofficial standard so you don't need to convince anyone of anything.
Sure, if my data is tabular I always end up with a CSV-like arrangement, usually space-separated. The original article however talks about how data always ends up hierarchical and tree-like. JSON represents tree-like data very succinctly and very readably.
Still, the real XML-killer for me is YAML. It's even more readable than JSON, and allows many documents in a single file. This makes it excellent for logs, or for any application where your files get big and you want to stream records off them without having to parse the whole file into memory at once. Sure, you can do this with XML and parser hooks, but it's so much more of a pain than just iterating over top-level YAML documents.
Another killer feature is that it's simple enough that I've been able to ask clients to provide me with information in YAML format just by giving them an example record to follow. They're non-technical, but they can read it as easily as me. That's a pretty big win.