Does a CPU heatsink need to cover the entire CPU package? (Xeon E5-1650, Arctic Freezer i11)

The part of the CPU in contact with the cooler is just a heat spreader. As long as the heat sink draws sufficient heat away from the spreader, it should be fine. Just be sure to watch the temperatures.

As you can see, the actual processor is quite small compared to the CPU package.

I used to have a cooler in that line with that same contact surface and it worked fine. Some additional tips: The part of the CPU you see is the heat spreader. The actual chip is usually a good deal smaller. Obviously contact with the entire spreader is ideal, but a sufficiently good cooler (which the Arctic Freezers usually are) can work with less. A good thermal paste will help a lot.

As others have said, definitely watch your temps with a good utility after you install it, but to expand on that point you should always watch your temps after you install a new heatsink. I'd be less concerned about the cooler's surface area and more concerned about installation mistakes. On some motherboards it's really easy to misalign or otherwise not get a good seat on the spreader. And keep watching those temps for awhile. Thermal pastes have a break in period that's usually around 24 (working) hours. If you don't use your machine all the time that can actually take awhile.

On the subject of thermal pastes, a lot of people are still recommending Arctic Silver 5. I prefer Prolimatech's PK-1. If you're very new or have tremors in your hands I recommend something like PK-1 or Arctic Ceramique. They're electrically insulating, so it's not a big deal if you get some on the traces on your motherboard.

I have a xeon in my workstation which I was surprised to see had the fan half off the CPU. I didn't install it, but here's an image. It has similar copper heat pipes.

I'm no expert and to be on the safe side I'd boot into the bios config and watch the temp to make sure it stabilizes and doesn't look like it's heading into the 100s.