In the In-Portal 5.2.2-B1 release a Plupload-based file uploader version was copied over from In-Portal 5.3.x development branch. One of the Plupload features is ability to pick upload way (html5, flash, html4), which will work best in current browser.
Due misconfiguration the "html5" upload way is never picked even if browser supports it.
Solution
Change "runtimes" option of Plupload (the "Uploader.init" method in "/core/admin_templates/js/uploader/uploader.js" file) from "flash,html4" into "html5,flash,html4".