Hi!
For SELECT queries, the response format is application/sparql-results+xml by default (even without specifying the format parameter), and the only other format I could persuade it to offer was JSON (with format=json).
Yes, the query supports only xml and json formats now.
For CONSTRUCT queries (the useful sort :-) ), you need format=rdf (or format=application/rdf+xml), which returns a lovely RDF XML document. If you omit the format parameter, you get a 'File not found' error.
For these, you can do both XML and JSON too. What you could do is run CONSTRUCT query, which would return JSON having three fields - subject, predicate and object - and then make a simple script in any language that reads that JSON and processes it to output, say, ntriple-formatted RDF. That would be not hard.
As this is just starting the SPARQL story, it would be nice to see suggestions about how we could format the output better... Maybe some export options in the GUI. JSON has all the data, but some processing is required to get CONSTRUCT produce some useful RDF serialization. At least for now.
BTW it's open source (the GUI too) so pulls to https://github.com/wikimedia/wikidata-query-rdf/tree/master/gui may also be the way to do it ;)