This is amusing in that I
very recently picked out a very similar pattern for some fabric I already have on hand. Here is a
video that shows how to put together the quilt with all the partial seams. (Your pattern would be a little different in that it looks you would first sew thin strips of of sashing fabric to your colorful fabric, but after that the construction should be like that in the video.) I expect that the video will be much clearer than written instructions.
The main downside of partial seams is that you need to do a little bit backstitching at the ends of seams to lock the stitches, so it is a
little bit slower than a similar project without partial seams, but not by much. Ultimately, you are sewing the same length of seams, you are just breaking it up differently.
Personally, I've done small amounts of partial seams, and I don't find them a hassle, so I am looking forward my project. For me, I would rather do partial seams more than some other quilting techniques, such as curved piecing. I suggest grabbing a few scraps and cutting out a few rectangles and trying out the technique. With just 8 rectangles, you could make two (very short) "braids" and then join the braids together. For your test, you can make the rectangles much smaller than the quilt pattern , say 4" x 2", so that you waste less fabric, but it should still be enough to give you sense of whether the technique is overly aggravating to you.
If you do find partial seams not to your tastes, you can easily alter the pattern to cut of the points on the sides of the braids and join the straight seams. (This will reduce the width of the quilt.) Here's some samples of that type of quilt:
Best wishes in weighing your options!