People sometimes added a heatsink to bridge chips like that, but those cards didn't come with one. Here's an HD3850 for an example:

So the card should work fine without this heatsink?

It is true that in the case of ATI I have never seen a graphics card with a heatsink on the bridge chip and they work correctly for a long time. But those bridge chips get very hot without dissipation and are a frequent cause of failure. In the case of nvidia graphics cards, the bridge chip always had a heatsink.
It is not easy to glue a heatsink to that chip because it is very small.

So maybe this was a mod by the original owner? Anyways, I'll try without the heatsink and see how hot it goes.
Thanks for info.

There are inexpensive kits for adding small heatsinks to MOSFETs and Raspberry Pis that come with thermal tape already installed - sticking one of those on that chip should be easy, and better than nothing if you're concerned about it.