The video card is no more magical than any other item inside or outside the computer. How are you reading this web page, you have at least two computers communicating with each other over an interface (ethernet/internet). Memory, pcie (video, hard disk, usb, etc), usb (mouse, keyboard, etc), network, are all connected to the main cpu via interfaces that are ultimately tied to the cpu's external interface (memory bus for lack of a better term).
We like to think that many of these devices are pure logic and that seems to make sense that when you write to some address that is routed to that peripheral that address and data tells that blob of logic to perform some action. But just like reading this web page on one computer that is served up by some other computer, it doesnt have to be pure logic, you just need an interface to move data. Not only a gpu but a number of other things in your computer have processors inside, the network interfaces might, the mouse and keyboard probably do, hard disk most likely, and as we now know the battery packs on laptops have a processor with firmware as well (mac batteries being infected with a virus that re-infects the computer after a clean re-install).
No magic. The software/firmware running on these other processors in your computer are not unlike the logic, a percentage of their job is to wait for commands from the main cpu to do things. Mouse please give me the button status. Gpu please draw me a triangle.
There are no special assembly language instructions in the cpu for video. The cpu doesnt know a video card from a hole in the wall, the driver knows/determines the address space for the video card it knows how to talk to, through that address space it writes the data values required to tell the video card to do things. Draw me a triangle may involve several items of data, no doubt the three corner coordinates, perhaps a fill color or is it straight lines which is likely just part of the definition of the communication interface with that peripheral.
There is no magic here, if you wanted to ask someone to do something for you you would provide a list of things for them to do and communicate in a way they could understand (go to 123 main street, ring the doorbell, tell the person that answers you would like two tickets to tonights performance, give them this money, return with the change and the tickets), with hardware it is easier as the communication interface is well defined for that peripheral.