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That's worded strangely (powering the lasers takes both 300 and 2.05 megajoules?) but oof
Powering the laser takes 300 MJ but the actual laser power (the energy in the light) is only 2.05 MJ. The rest of the energy is lost to heat and other inefficiencies. If the laser could be created with 100% efficiency then the input energy would also be 2.05 MJ.
Energy can be measured as occurring in different physical phenomena. There is energy in sound waves/packets, energy in light waves/packets, energy in matter, etc.
The 300 MJ number refers to the electrical energy in the form of electromagnetic fields carried specifically through solid conductors via electron movement along the conductors.
The 2.05 MJ number refers to the radiative energy in the form of electromagnetic fields sent specifically through free space/a vacuum (I presume; I didn't read the article, so maybe the laser medium was a vacuum or something else) via photons/waves. No electrons, aside from those in the lasers that create the photons in the first place.
So there is a conversion from electric to radiative energy here.
Start Edit:
And as another commenter said, in this conversion there are losses because materials aren't perfect.
:End Edit
If the 3 MJ radiant energy from the nuclear material was then converted back into electric energy via steam processes, we'd get a comparable number compared to the 300 one.
This is also why you see nuclear/CSP plants quoted in MWt and MWe: there is a conversion that takes place from thermal energy (vibrations of atoms/compounds) into electric energy.