Given the above, if you have two engines with same max power output, one with higher low-end torque will win a drag race
Right answer but wrong explaination. The engine with more power at low RPM wins the drag race because it can put more energy in an object in less time.
Explanation is correct. See below.
Accelleration is about energy. Not torque. Torque is defined as N/m.
Acceleration is about force and mass, not energy (Force = Mass * Acc). Torque unit is N * m (Newton * meter), not N / m (Newton over meter).
There is no energy and/or time relation in those units and therefore it cannot be used to compare time related performance.
Torque, power, energy, RPM, time - all those units are directly related in example of ICE and drag racing. Power and torque curves w.r.t. to RPM show engine performance in different, but completely exchangeable ways. If you know power curve - divide by RPM and you know torque. If you know torque curve - multiply by RPM and you know power.
Physics 101: energy is not pushing a car. What is pushing the car? Car is pushed by force. Where is this force coming from? Force is a torque. Engine generates torque, torque is transmitted via gearbox to wheels (with some transmission ratio - torque can be higher or lower at wheels than engine torque) and to the road [torque is converted to linear force].
What is energy? Energy = Force * Distance ~ Torque * Transmission ratio * Number of rotations
What is power? Power = Force * Distance / Time ~ Torque * RPM
Back to drag racing example.
EDIT: Example about drag race assumes that all conditions (friction, mass, tyres, gearing, etc.) are the same except engine torque at low RPM.
/EDITCar with higher low end torque will accelerate faster because it is pushed with higher force. This also means that at first moment this car will get more instantaneous energy (power) than the other and wins.
Example can be viewed from torque perspective (more torque -> more force -> more acceleration -> more speed) or from power perspective (higher torque at the same RPM -> more power -> more work done in the same time -> more speed).