MP3s with tags inside that cannot be read by MP3TAG

I have examples of MP3s whose tags cannot be read by MP3Tag for some reason. The tags are definitely in, you can view the file and see the strings with the title, composer etc. inside. Other tag editors (ID3Tagit and MP3Tagit) also see them and allow their editing.

I packed some of them together in this file:

You have APE tags in the files, probably from replaygain - and that program only wrote its own tags but did not synchronize the field contents of other tags.
Check Tools>Options>Tags>Mpeg
whether you read APE tags - if so, switch off that option and re-read the files and see whether all the data is back again.
If the APE tags do not contain anything important, delete them.