But now I cannot import it. When I look at the export in word, only the source and the target languages I had set in MT 6.5 (188.8.131.527) have been exported, but not any of the other languages.
Do I need to prepare a new export definition for this purpose?
You may have to - my own termbase only contains German and English, so I cannot contribute own experience here.
Any suggestions? Can I also simply save the export file in .txt when I use a different export definition, such as the "Default export definition" which lets me make a back-up?
Nope - although in substance, XML files are text, the structure differs considerably.
Have a look at the export file; my hunch is that the language codes don't match; you may have to tweak the export using search and replace.