what is the process for obtaining a Chinese tourist visa if I am an American living in Seoul?

If your ARC has at least 6 months validity, you can apply for a tourist L for China and it can be issued. Otherwise, you cannot apply in Korea.

For applying, you need to take your valid passport, application form with recent taken photo, hotel booking in China, round trip tickets to China and your ARC card to apply through the nearby CVASC.