This discount requirement can be used with any other discount type.

To use this discount rule, the discount requirement type should be configured as Discount on selected weekday and need to provide value for weekday on which you want this discount rule to be applied to as displayed in the image below. 

on selected weekday discount requirement

Once saved, the discount requirement will be added to the discount as displayed in the image below.

on selected weekday requirement

That's all you need to do in order to use this discount requirement in your nopCommerce store.