If weightlifters lift their weights up and down, and thus do no actual "work" are they truly "working out"?

Yes, Weightlifters are truly working out.

Explanation:

Definition of work in physics is the transfer of energy when an object is being moved. But, when an object is being lifted then net work done is zero because of the gravitational force acting on it. But, if we speak in terms of transferring energy then there is a workout. For example, if you push a bench and it moves. there is a transfer of energy to the bench and it moves. Here, when you lift a weight, it burns your calories and also there is a movement for the weight also.