Yeah, I don't know what to make of that dad.
Except that, commonly, men and women alike are raised to take for granted that housework and childcare are primarily the wife's responsibility, regardless of whether she works outside the home. At least, that was true in my generation. I had hoped that things would improve in my children's generation, but apparently they haven't, yet. The helpless dad in the article is just an extreme example.
I hear you, about being a working mum. My kids are mostly grown now, so I've had it easier than it would be if they were younger, but housework is eternal.