Full Wave Rectifier Efficiency
The writer of your reference article has himself defined the efficiency differently than usually. In his lossless circuit (=transformer, diodes, resistive load) all power taken from the mains voltage goes to the load, but only 81.2 percent of it is DC, the rest is the AC component. The load gets it, too. It's not wasted as dissipation in the rectifying circuit.

Writer's definition has some meaning, if we could have a filter that only removes the AC component from the output voltage without any side effects. Inserting that filter causes the power to the same resistive load drop 18.8%. Is that drop lost as thermal dissipation -yes, if the filter dissipates it.

In practical circuits, especially if the  filter is not dissipative, then the power drop is difficult to to know without complex calculations.

ADDENDUM: Commentator @Dave Tweed is right. A lossless filter and diodes interact non-linearly, waveforms get distorted and the action changes radically when compared to original with resistive only loading => the presented "efficiency" 81.2% loses its meaning.