So, I just looked it up, thinking I might have overlooked something but, at least according to wikipedia, REST does not prescribe the format of the data transferred. So, I don't understand why you are comparing REST to xml, yaml, json or whatever.
Now, YAML has quite a few shortcomings compared to JSON (if you don't believe me, look at its handling of the string no, discussed on HN), so, at least to me, it's obvious why JSON won.
SOAP, don't get me started on that, it's worth less than XML, protobuf is more efficient but less portable, etc.
XML has been supported in javascript for essentially just as long as JSON, arguably longer. Heck, the first in-practice and standardized HTTP request APIs for javascript were "XMLHTTPRequest" (and similar "XMLHTTP" names). And XHTML is a thing, and it predates both JSON and AJAX.
Not just XML, but a lot of other serialization formats and standards, like SOAP, protobuf in many cases, yaml, REST, etc.
People say REST won, but tell me how many places actually implement REST or just use it as a stand-in term for casual JSON blobs to HTTP URLs?