Yes, reinforcement learning (and, in particular, bandit) algorithms have been used to solve (real-world) problems other than games, such as

- [Recommender systems][1] (actually used in practice, e.g. see [here][5])
- [Portfolio optimization][2]
- [Clinical trials][3]
- [Hyper-parameter optimization][6]
- 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][4] (2019) for more ideas and answers.

 [1]: http://rob.schapire.net/papers/www10.pdf
 [2]: https://arxiv.org/pdf/1909.09571.pdf
 [3]: https://www.pnas.org/content/pnas/106/52/22387.full.pdf
 [4]: https://arxiv.org/pdf/1908.06973.pdf
 [5]: https://azure.microsoft.com/en-us/services/cognitive-services/personalizer/
 [6]: https://arxiv.org/pdf/1611.01578.pdf