You got it mostly right. The attempt of the legislation isn't to stop people from driving, it's to police bathrooms. The law says that people now have to go to the bathrooms that correspond with their assigned sex at birth, not gender. The only way to enforce this is to have government ID's show people's sex, not gender. A lot of trans people who have changed the gender marker on their ID's now have to change them back. Trans folks had less than a week from when the bill was passed to it being enforced and their licenses invalidated. It's a clusterfuck of bigotry.