Well, I dunno what to say about this one. Regardless if I play this .WAV in VLC, Winamp, etc., it sounds identical to the original demo song when played in Renoise.
To confirm that nothing weird was in your .WAV file, I just rendered my own version from the original demo song itself, and then compared the two waveforms in SoundForge. They appear to be identical. So, in my opinion, whatever strange stuff you are hearing is NOT present in the actual waveform, and is not coming from Renoise.
I know it’s already been discussed, but you should double check VLC itself. It has various options for signal gain, EQing, surround sound, etc. Just make sure that everything is set to default/flat settings. Any kind of EQ or gain could be causing you to hear something weird. Try playing the .WAV in other players like Windows Media Player, Winamp, Foobar, etc. Do you hear the same problems there? If you hear the same problem from several different media players, then it must be caused by something in your audio setup.
What kind of sound card do you have? Does it has some kind of EQ, filters, effects, surround sound, etc., that can be applied to its master output? That kinda stuff is very common on SoundBlasters and similar cards, and if you have anything like that enabled then it should definitely be turned off while making music. Even if it’s just a simple EQ adjustment to boost the lows/highs a little bit, disable it.
What kind of speakers do you have? What kind of amp/receiver is driving them? Are there any EQ settings there you could reset to default/flat settings? Etc.
Regardless of the fact that the pro tracks you are comparing against do not appear to be affected by the problem, clearly there is something else going on here.
[Edit]:
Just checked the 2nd .WAV you posted now. I do not hear any kind of ringing or strange artifacts in this, either.