The ability to use XSLT to convert JSON to HTML may be useful when making extensions for working with web sites that internally use JSON. Converting XML to JSON might also be useful for some things.

However, XSLT would be useful with command-line programs too, and not only in a web browser, anyways. (A standalone implementation might also be made to have the ability to load extensions written in C.)

There are problems with XML and with JSON, as well as with XSLT, but when dealing with XML and JSON formats anyways, XSLT can be helpful. (One problem is that XML does not deal very well with types other than Unicode text (JSON has a few additional types but still not very good). XSLT does add some types, though.)

They also mention RDF, but the standard XML format for RDF is not very good in my opinion (although I think someone did make up a better XML format for RDF, for the help of being used with XSLT better).