It probably was not done by hand, but as the WAD file format is pretty well documented it was probably relatively easy to write a one-off tool to perform the conversion. It's possible one of the WAD editors floating around have the functionality buried away, but I suspect that the author used a tool he wrote himself (and has not released) in this case.
The JSON structures and arrays used in the linked JSON file don't seem to correspond directly to the lump types in the WAD file, which suggests a custom tool to me. It looks like some of his maps aren't direct ports of DOOM maps either (at least none I recognize) so it's possible he's using an internal map building tool instead of just an internal JSON conversion tool.
The author's email is at the bottom of his homepage. You'd probably get a better response if you ask him directly.