The slip angle experienced during a crosswind take-off is going to have two major aerodynamic effects.
The upwind (i.e. into wind) yawing moment caused by the directional stability is one of them, and it's counteracted by rudder, or steering, depending on speed. But there's also a downwind slip force. If you're in the air, it's easy -- you bank upwind to provide an equal and opposite force, and you have a sideslip. But on the ground, with a constraint to keep the wings level until you rotate, the only thing stopping the aircraft from moving downwind is the lateral force from the wheels. Thus in a normal situation, crosswind might be limiting either through lack of rudder authority to keep it straight and avoid leaving the runway upwind, or through lack of weight on wheels to keep it from drifting off the runway downwind.
Engine failure will mitigate (downwind engine fails) or exacerbate (upwind engine fails) the total yawing moment that the rudder has to handle, and therefore the upwind engine is critical. You might naively think that the opposite would apply if the drift downwind is limiting. But, with wings level and tracking straight, I can't see why either should affect the lateral force, and I therefore can't see how Flaperon can justify "To cut a long story short,the downwind engine IS the critical engine in case of EO".