You’re right. It was first introduced with the PS2 in 2000. I do however have a vague recollection of early cartridge based systems where you could download games over cable.
You're probably thinking of Sega Channel [1] which was functionally like Microsoft's Game Pass that is available now. You knew that you would only have access to the games as long as you subscribed, and that they could be changed at any point by Sega.