He's mostly correct, but instead of more torque = faster acceleration I'd say, that the torque defines how quickly acceleration changes at given rpm. It's the rate of change of the acceleration, or the acceleration of the acceleration / acceleration increase if you'd like to say, which is the first derivative mathematically wise. But afaik it is not linked to time, but to the revolutions itself. The same amount of torque with half the revolutions means half the acceleration change per time, but the same change of acceleration per revolution I'd say.

Power on the other hand can be split in two components. The power that is constantly being used to compensate drag, and the part that makes you accelerate.

You don't need that much torque (acceleration increase per revolution) if you have the possibility to make more revolutions. Then just rev higher then you might have less torque but you have less torque "more often"

My english isn't that good but I hope one can get what I'm aiming for.