Looking at the pictures, and from having observed various ATI cards from that and latter era (e.g. X1950 Pro, HD3870, and HD4870), I am like 99.9% certain both of these caps are for the GPU V_core output filtering. If that's the case (you should verify, of course, see next paragraph below), then there shouldn't be a problem to use the card as-is. I agree it's not optimal, but it won't cause any damage to the card. Worst case, a noisy GPU V_core voltage might cause crashes or almost invisible artifacts that don't make anything crash. But in most cases, that won't happen at all, simply because the filtering of the GPU rails is designed to have some overhead on the permissible noise levels. Thus, loosing a few filtering ceramic caps that are for filtering won't cause any issues usually.
That said, it is a good idea to verify that these caps are as what we suspect they are. You can do that very easily if you have a multimeter: just measure the resistance across the pads on the two missing caps. If both show the same (likely very low) resistance, then they are all connected in parallel and probably part of the GPU V_core filtering.
@tehsiggi suggested that one of these caps (that appears to be alone) might be part of the VRM bootstrap... but I find that unlikely, as bootstrap capacitors are not usually placed nearby and/or on the same large traces that are part of the power rails in order to avoid injecting noise into the VRMs. Usually they are more likely to be close to the PWM controller itself.
The fact that the card works fine, however, suggests that everything is probably fine. But again, just verify with a multimeter if you have one. You could also measure the voltage on the pads of the missing caps to verify if they are on the same rail. However, I usually caution against this unless you are experienced and/or have very steady hands, as it would be easy to slip the probes and short out something and cause more damage. In contrast, measuring the resistance should be much safer, because you do it with the power off / card removed from the PC.
If these caps are indeed part of the VRM output (or perhaps maybe input?), my guess would be that they are in the 4.7 to 10 uF range, and probably rated 10V minimum to 25V max, depending if they are on the input or output.
