What can cause this damage to the GPU?
The on each photo, the central part looks hand-soldered to me. On the last two pictures for example the excess amount of burnt flux is visible. Also while the components do no appear to be beautifully soldered, I don't see why they wouldn't work because they all appear to have electrical connections. 

If nobody tried to hand-solder the components, it may be possible that someone tried to bake the card and may have added extra flux to the components to make the process go more smoothly. If that was the case, then we're probably not seeing the main damaged area. People usually bake cards when they believe that the solder balls on one of the BGA chips (and that's usually the GPU itself) are cracking and have bad connection. Unfortunately from what I've heard the only relatively cheap way of seeing the damage there is to make x-ray images of the card itself and even then not many people would go through the trouble of actually replacing a BGA component. The damaged capacitors also in my opinion support the baking idea since they can easily be overheated during the process and leak or explode.

If the card really wasn't "repaired" by someone else, then only thing that could in my opinion cause such problems would be really really bad overheating. There are stories of SMD resistors for example desoldering themselves because they heat up too much, but then again you have some problematic capacitors too.