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”“deprived of the ability to move". A creature has only been deprived of the ability to move when they cannot choose to move, or could not have chosen to move. This is why a flying creature does not fall after expending all of their movement on a turn. If a creature choosing for themselves to do something that later prevents them from moving is the same as being "deprived of the ability to move", as Kirt argues in his answer, then a flying creature who expends all of its available movement on a turn falls. By expending all of their movement, they are no longer able to move, and have thus deprived themselves of the ability to move. Obviously, this is a silly conclusion, a flying creature should not fall at the end of every turn that it expends all of its available movement.
Ergo, they do not fall, even if they choose to take an action or bonus action.
That said, I must admit that there is plenty of room for the DM to rule otherwise. Kirt’s answer outlines the alternative argument.