yes, they do. $1 per day, the rental itself is $1.20 though. hope this helps.
On your first visit to Redbox (or the first time you use a new credit card at Redbox), you can rent a maximum of 3 discs, 1 of which can be a video game. Customers who have rented from Redbox before can rent a maximum of 5 discs, 2 of which can be games.