Okay, after another bunch of tests I nailed it down to the relation between vertices of the model and the vertices needed for its skin.
When their numbers are identical, then everything is fine.

http://www.puppenheim.org/
http://www.wuerfels-welt.de
Old Game Tutorial: http://www.puppenheim.org/MITutorial.zip
Free Game Editor: http://puppenheim.org/AlienalsWeihnachtsmann.zip
http://www.puppenheim.org/blender_starting_main_settings.txt