Hi Christoph,
I suppose the first thing would be to check whether this is a general problem with the SCORM packages - you could maybe try signing up for a free account with something like https://cloud.scorm.com and see if the packages work correctly there.
If they do work on scormcloud, then it is likely to be either a problem with the Moodle scorm player; or one of the themes.
You could try it on a quick install of vanilla Moodle from moodle.org; and also try switching the themes between standardtotara, totararesponsive, kiwifruit etc to see if the problem is across all of them, or only on a particular theme because it may be an obscure theme/CSS problem.
Also in IE 10 using the developer debugging tools might point towards a javascript or other error:
http://msdn.microsoft.com/en-us/library/ie/hh968260%28v=vs.85%29.aspx