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Not sure this is useful but that segment is part of season 2, episode 4 of the show. Released in 2002. At the end, Productions MAJ, Inc. is credited for the Animation segment... being the creators of the show How it's Made as well, they've credited themselves on that one — so if anyone can find a listing of what other things they've done, it's possible this animation short will also pop up.

Further details:

• There are glimpses of a script at the beginning of the segment, that shows two characters talking with each-other, a "Mr. Mackintosh" and "Mimi", in English (possibly unrelated with the rest).
• The software used for 3D modeling, animation and lighting, is Softimage, with two versions of it being clear to have been in use, the pre-2000 version, and the post-2000 version, called Softimage:XSI since. Its notable characteristic being: the black wireframe in dev-view, and also, the rigging aids for animating characters.
• The final animation we see, looks like it has volumetric lighting/effects (when that girl? jumps on those boxes), this seals the deal for it being rendered with Mental Ray, only available for Softimage at that time.
• This all makes the animation probable to have existed somewhere between 1998 and 2002.
• But if you look at the animation, there is a glimpse of the girl? being frozen in slowmotion midway through her? jump and a slight camera surround pan on her?, probably a Shout-Out to The Matrix, so maybe 2000 onward.

edit: minor corrections