Question: I know there are devices to measure power (e.g., dynamometers) but I can't think of any example of a device that measures work directly. Is there such a thing?

Answer: 
Several things that we don't normally think about as "work meters" effectively measure work.

For instance, if you marked a spring scale with energies instead of forces, you would have a device that measures work done to it.
If you've ever lifted an object on a pulley, the height of the object functions as a 'work meter'. 

Another way to measure work is to convert the energy to heat and measure a temperature rise, which is the principle behind calorimeters. 

A third method is to indirectly use chemistry. You can calculate the total energy released by a battery given the energy released in each individual reaction. Similarly, you can loosely estimate how much work a human is doing by seeing how much $\text{CO}\_2$ they exhale.