Automatic is cognate with autonomous and often contrast against manual and while I do object to the use of the word manual for anything that does not involve the use of the hands, in the case of a car the word is apt because the primary method of directing them involves the use of the steering wheel, which is hand held.
Additionally, it is a very natural progression of terminology, in large part because we are already distinguishing between automatic and manual transmission, so manual is a word that is likely to come to mind by anybody caring to make the distinction.
Driving a car with a manual transmission—also called a stick shift—requires more skill and understanding than operating a vehicle with an automatic transmission. In a stick shift vehicle, you will be manually shifting gears to adjust your speed, rather than letting the car do it for you.
However, rather than manual cars, I would imagine that these would be called manually-driven cars which uses an adverb to modify a past participle to form a sort of compound adjective to describe the cars. Manually driven is not a very new term, and as a matter of fact, this seems to be the terminology which is already in use for this purpose:
Simulation studies by Minderhoud and Hansen show that the application of automated trucks on a dedicated lane using the platoon concept is possible, although additional traffic control measures are required to ensure safe crossing of manually-driven vehicles with the automated trucks. [Emphasis my own]
It is also possible that automated cars in the future will have manual-override for cases when a properly trained human driver wants to go somewhere other than a predestined location, or ascertains that the automated driving is going haywire. In these cases the distinction between autonomous and manually-driven cars may be rendered moot, except for historic contexts.
1 How to Drive a Stick Shift by the D.M.V.
2 Page 9 of The Future of Automated Freight Transport: Concepts, Design and Implementation (© Rob Konings, Hugo Priemus, Peter Nijkamp 2005)