Yes, reinforcement learning (and, in particular, bandit) algorithms have been used to solve (real-world) problems other than games, such as
- Recommender systems (actually used in practice, e.g. see here)
- Portfolio optimization
- Clinical trials
- Hyper-parameter optimization
- Self-driving cars (although I am not aware of any real self-driving car that uses just reinforcement learning; however, in principle, RL can be used in this context too)
Take a look at this pre-print paper (2019) for more ideas and answers.