Thanks for all your comments! It's nice to know that we're in a community, doing research and craftwork together!
I really do not pretend to have the “definite” answer, but I'm inclined to think that it's embroidery rather than knitting. Chris L., thanks for pointing the Spanish pillow out to me and dropping the word “long-armed cross stitch! This reminded me of some sources that were “sleeping in my archive”. I happened to make a scan of the Spanish pillow some time ago, which clearly shows the changes in direction you refer to. The changes are not only at the edges of each square, but also occur within the heraldic motives. With my knowledge of knitting, I think it's technically not possible to change directions like this.
Image from Gomez-Moreno, M (1946), El panteon real de las Huelgas de Burgos, Madrid: Consejo superior de investigaciones cientificas, Instituto Diego Velazquez
There are two papers on long-armed cross stitch by the Westkingdom Needleworkers Guild. Do take a look at them, because they also contain pictures of the Spanish pillow and a close-up of a purse in long-armed cross-stitch which looks very similar to that blogged by Racaire (this close-up also shows the surface “ridges” which surprised me so much)
Westkingdom Needleworkers, thanks for these papers!!!
So, it may be long- armed cross stitch (or a chain stitch?), which allows you to changes directions
Racaire also suggested the technique might be similar to that used in a “Codex Manesse” pouch. I saw this pouch a few years ago, fell in love with it instantly, and made a copy myself :-). This pouch is made using “versetzter gobelinstich” and couched goldwork.
A picture and a description of the original can be found in:
Schneider, J. (1975), Textilien. Katalog der Sammlung des Sweizerischen Landesmuseums Zurich: Zurich: Verlag Berichthaus
The Cloisters Museum, New York, owns a similar purse, see here: Hoving, T., Husband, T., Hayward, J. (1975), The secular spirit: life and art at the end of the Middle Ages, New York: The Metropolitan Museum of Art