Catalysis of the reaction: reduced coenzyme F420 + 2,3-dimethyl-1,4-naphthoquinone = coenzyme F420 + reduced 2,3-dimethyl-1,4-naphthoquinone. Reduced 2,3-dimethyl-1,4-naphthoquinone is also known as 2,3-dimethyl-1,4-hydronaphthoquinone.