Hi Tõnis,
I'll not solve your problem I'm afraid, but I can say that I'm running Moodle 2.3.1 over https:// and for me dragmath works fine.
Is there some kind of java debugging console or sth. that can tell you what the problem is? Often useful information can also be found in the web server logs, at least in case the pages are served by apache.
Greets, Mikael