It is designed to be played with cartridges. That’s kinda the point in that it lets you play your original carts on a modern TV with perfect simulation of the original hardware.
That said, it will likely play ROMs too. The two Turrican games that ship with it are provided digitally and it accepts SD cards for updates. Without getting into a piracy debate, it’s likely that you could play games without buying them, but the point is kinda that you can play the carts you own.