If you're a professional game designer, it's essential to learn about the basics of every aspect of game development! Every discipline is important, but today I will focus on why it's helpful to understand visual artwork.
Having a working knowledge of 2D concept art can give you much higher-bandwidth communication with artists. For example, Aubrey is an awesome artist, but he can't read my mind; if he draws a character or object that is not compatible with the design I am thinking of, we need to be able to speak the same language in order to change the design and the character and bring them closer together. Sometimes I have ideas or suggestions that can be communicated more efficiently with simple sketches than with words. Here's an example of a 'greenline' drawing I did when Ian Wells was working on the old rabbit model.
Also, drawing reference images is an effective way to make sure that you have looked at and considered every part of the image in detail, which can help come up with ideas for parts of the game design. I was having trouble thinking of interesting ways to make the rabbit characters look different, so I sketched some rabbit faces to get a better idea of how they work:
Whether you're making a 2D or 3D game, it's important to familiarize yourself with the artist's pipeline for creating game assets. That way you know what questions to answer. How many polygons should the model be? How big is the texture? Does it need normal maps? Is it seen from all angles? Without an understanding of which questions are important and how to answer them, it is not possible to ensure that the assets are created efficiently.
If you know how the assets are made, you can come up with rough estimates of how long each asset will take, and can more closely match your design's artistic needs to your art team's capabilities. This can help reduce the risk of going over-budget or hiring more artists than you need. Finally, if you understand how assets are usually made, you have the freedom to change the process to make it fit better with your own project.
At Swarthmore, I took a game development class in which we formed small groups and worked on very short game projects. In my group I volunteered to be the artist and sound designer in order to try and expand my skill set. Here is one of the low-poly characters I modeled and animated:
None of my artwork is good enough for real production, but I think it's good enough to allow me to communicate with artists, and to design games that use art assets efficiently! Those are the main reasons I can think of for why game designers should learn to draw. Please let me know if you can think of any other reasons!