Thanks. My browser tried to play the file instead of downloading it (that's why I asked to zip it), but I found the file from the browser's cache.
The ID3v2 tag block is not correctly readable by some programs, including Media Center, Mp3tag, dbPowerAmp, Windows Media Player and foobar2000. These programs can see only the ID3v1 part, which doesn't contain cover art or they can access the ID3v2 tags only partially. As you said, some other programs can read the ID3v2 tags and the included APIC frame, which contains the embedded image file.
The ID3v2 tag format appears to be slightly invalid and not all programs seem to be able to handle this.
I don't know if JRiver can change their code to support this kind of file (I let Matt from JRiver answer this), but as a workaround you could resave the tags once with your Tag&Rename program. Any small tag change would be enough for making the files standard conforming. (I tested this by tagging ''LAME'' in the ''Encoded By'' field in T&R.)