The article doesn't say HDF5 isn't chunked, but that's the impression a reader might get if they don't already know better. It's certainly not the author's fault -- just an easy mistake for a reader to make with the flow of the article.
It's more that I keep hearing that statement ("Zarr is chunked and HDF5 isn't") in the wild a lot.
As for threading, yeah, HDF5 can be a bit cumbersome there.
I'm not sure I'd agree on compression, though. HDF5 supports fully arbitrary compression, after all, it's just the client reading the data also needs to have the compression filter you're using installed. Zarr is often used with BLOSC, and that was originally developed specifically for HDF5, FWIW.