Currently the endpoint GET /crosstracker_query/content
(and all the others under /crosstracker_query
can only be used if you know the ID of a widget. This prevents a pure REST API usages because the REST API does not let you create widgets and anyway it does not make a lot of senses to create a widget somewhere if you only want to fetch data.
It should be possible to query the endpoint GET /crosstracker_query/content
without providing a widget ID. Queries done without a widget ID should have the same behaviors than queries made from a Cross-Tracker-Search widget on a user dashboard.