it's basically just annoying bullshit
basically the enthalpy of formation is separate from the bond energies themselves, it's just how much extra energy it takes to create from the standard forms of the elements. the trick is that the standard form of oxygen is already O2, as it's how pure oxygen exists in our world. (whereas bond energies supposes the atoms weren't bonded at all, in an extremely unstable fashion) so the enthalpy chance from O2 -> O2 is 0, even though it breaks intuition.
wrt. the reactions, it's unrelated again, in most things you want to dodge touching binding energy entirely and just work in terms of enthalpies. Hess' law: delta-enthalpy-of-reaction equals delta-enthalpy-of-formation-of-reactants minus delta-enthalpy-of-formation-of-reactants. binding energy would work, but the thing is that binding energy of formation is actually really hard to find, obviously; you'd have to actually break the O=O bonds.
tl;dr the enthalpy of formation is zero, the binding energy is non-zero, the guy you linked is a moron and all the values he quoted relate to enthalpies of formation rather than bond energies
disclaimer: i'm not sure of any of this make sure you add salt and get a second opinion