Yes, of course.
Even though I write unit tests according to TDD (test driven development) most of the time and run regression tests when new features are introduced, there are lots of functionality (and non functional requirements) that are hard (or impossible) to test automatically. There are also cases where it is possible, but preferable to test by exploratory testing. Almost all "ility" requirements, such as usability, availability, operability, stability etc. are best tested using exploratory testing, and exploratory testing done right means trying to break your application any way you can think of (and not think of by performing random actions).
One lecture that I find very motivating and interesting on the the topic of exploratory testing, and "testing to break" is this one by James Bach: https://www.youtube.com/watch?v=ILkT_HV9DVU
It is not about testing games in specific, but rather about testing in general. He knows what he is talking about when it comes to testing and he is fun to listen to, even if he comes across as a bit odd at times.. xD