The affected creature is not “deprived” since they can choose to move or not.
At any point prior to taking a bonus action or action, the creature is free to choose to move. This means that the creature is choosing not to move when they instead choose an action or bonus action. Because they are free to make that choice, to move or not to move, we cannot say that they have been “deprived” of the ability to move. Ergo, they do not fall, even if they choose to take an action or bonus action.