I tried your file again using FX file manager and I get the same results, smooth playback entire time.
I have a tivo, TV and a computer hard wired on my network and only my table uses my wireless connection. Have you tried using Media House that I mentioned in one of my other postings, you may get a different result and it shows album art and shows a photo from video as an icon.
Using Media House, I got smooth playback after copying a file to my NAS box (Media House did not recognize my PC as a media repository).
Then I used MX Player via FX to play the same video from the NAS box and the audio problem appeared as usual. Aimed MX via FX at the same video on the PC just to be sure and got the same bad result.
Media House's introduction dialog contains words to the effect of "Media House does not play video itself, instead it uses one of your installed video players.".
When using Media House to play the vid, I selected MX Player from it's menu - getting good, clear playback.
Looking at it from the outside, that's telling me that the problem is somewhere in the way that FX reaches out over the LAN and retrieves the problem file that it then feeds to MX Player. Media House must use a different method of getting the data before it feeds the same file to MX Player.
That still leaves the puzzle of why your FX file manager gives smooth playback, but at least it seems to localize the problem somewhat.... and also explain why the laptop with Windows Media Player works.
My FX is v188.8.131.52. Seems to me like, somewhere along the line, I paid extra for network access; but I cannot find anything like an add-on in my ApplicationManger's list, so I must be wrong. All I have is FX (14.45 MB), FX Key (129 KB), and FX Root Access (40.00 KB).
If I can figure out how to make Media House recognize my PC as one of it's repositories, I might have a workaround. I don't have enough free space on the NAS box to move my recorded TV there.