The upwind engine is critical because...
You need rudder to counter crosswind on takeoff, and;
You need rudder to counter engine failure on takeoff.
If you need the same rudder to counter BOTH, you run out of it faster... An upwind engine failure will require more rudder than a downwind engine failure because you already need some of that rudder to counter the wind.
On a maximum weight 747, with maximum crosswind, and a critical engine failure (outboard upwind) at V1, it is impossible to remain on the runway.