Q: I’m trying to get the WPGlobus translations for my posts using JSON. Is there any way to show it?
A: You can use https://wordpress.org/plugins/rest-api/
To get page id=2 in default language ( in my case – English )
yoursite/wp-json/wp/v2/pages/2
To get page id=2 in German
yoursite/de/wp-json/wp/v2/pages/2
UPDATE:
Starting with WP 4.7 you don’t need to use https://wordpress.org/plugins/rest-api/ plugin.