According to this chart, women do about 9 hours more "unpaid labour" than men. 
Yet men do on average 50% hours more "actual labour" than women. Working between 7 and 12 hours more per week on average.

So even if we agree that loading the washing machine is labour (which I don't), there's between a 1.5 hour deficit, and 3.5 hour surplus.

So even if we fully agree with the premise that all of these things are justifiably "unpaid labour", it's still not true.