Yeah, now that I have time I see it's a variation on earlier ones. For each triplet of color squares (row or column), a given color must be in each row and column of the square only once. So for the right column of color squares, yellow isn't present in the left column or middle row, so must be there in the solution. Red isn't present in the right column or middle row. Magenta isn't present in the middle column or middle row. Etc.

They do have some higher-order patterns that aren't necessary to solve it. There are three distinct groups of colors, blue/greens, grays, red/yellows, always in a row in a given square. Each one has the same order of colors from left to right, and they are merely rotated horizontally (wrapping around). For each row or column of color squares, red/yellows always rotate right (going right/down), blue/greens rotate left, and grays rotate right. Then the rows themselves all move down when going right on rows, or up when looking down a column. This higher order seems lost on the above simpler solution. They could have not adhered to this and still had the simpler solution work.