The article was clearly written by an enthusiast, but is a bit muddled. I see nothing in what he has written that supports the idea that Color Wheels are wrong.
Color wheels are, in essence, highly abstracted slices across the equator of a color space. Only two color wheels are commonly used: the RGB and the RYB (aka the artists color wheel). Color from pigments and color from light are two wildly different things, but easy to confuse. For its absence of green as a primary, CMYK can be understood as a version of RYB. Black is used not just because it is cheap but also to add opacity to the inks (printing inks are more like dyes... very thin and transparent).
The color opposites the author describes are red/cyan in RGB and red/green in RYB.
One property of these opposites is that they mix to neutral. For this, the RBG pair works best. The other property is that they are perceptually antagonistic, for which the RYB pair works best.
Interestingly, the perceptually antagonistic pair set (red/green, yellow/purple, blue/orange) were spoken about well before Newton placed these colors in a circle. Leonardo Da Vinco refers to them as 'retto contrario', literally exactly opposite.
The author asks 'why a wheel'? which is a good question, and the answer he gives is reasonable. But... Newton was the first to employ this device, and he did so almost certainly because the harmony structure of the musical scale was commonly visualized as a wheel, and Newton was keen to draw an analogy between music and color and harmony and the music of the spheres and god etc etc. He may have been the first physicist, but he was also an alchemist.
Color is a frustrating beast... so many different ways to understand the same thing: perception, physics, aesthetics, chemistry etc. Truly the seven blind men and the elephant.