It looks like an onboard GPU chip on the motherboard.
It has 64MB of graphic memory as opposed to 2GB. Speed will be lost as different software competes for memory. Updates to the screen will be routed through the CPU.
The nvidia gtx 550ti is quite old so you might be worth buying the latest version with as much memory as you can afford. This will future proof the system. If the computer is old it might be worth replacing the whole thing and specifying the 550 as the minimum required.
Thanks for your reply cdtaylornats. Final question, are these things fairly easy to install? I'd probably go for the old model as newer ones seem to be so expensive. Long term, I think at some point I need to look into buying DS a computer built specifically for gaming.
Google the manual for your computer. Read it to figure out how to open the case, open it and see if there are any spare slots for cards (manual will tell you where those are) and what type they are (PCI-E, PCX etc). Then decide whether you want to either buy a new graphics card or just upgrade to a new PC. The Nvidia GTX 550 Ti is discontinued, it is 7 years old - you could try a GeForce GT 730. If there is a local PC repair shop you could try asking in there, somewhere like PC world wouldn't have an idea and will just try and sell you something.
The game sounds quite old if its referring to this GPU, if your DS gets into gaming and you are happy with that, he is going to need a new PC soon anyway.