If retailers such as walmart and target find that inventories are rapidly being depleted, would it have been caused by a rightward or leftward change in the aggregate demand curve? what are the likely consequences for output and investment?

To deplete is to reduce in quantity, so if a product depletes it means the demand of that product has increased, and an increase is represented by a rightward change.

The likely consequence would be to order for new products, there may be stock out costs such as loss of goodwill, loss of sales etc. Investment would increase for that product and period to exploit the sales better and increase earnings, so money would be spent to order, transport and store the product.