Anyone can learn game theory, the key is how to learn and how deep to learn.
Liberal arts students can only understand some concepts and classical conclusions of game theory, such as Nash equilibrium, prisoner's dilemma, complete information game, incomplete information game and so on. They can learn from some concrete and vivid examples, without looking at those cold formula derivation and over-formalized expressions.
To ask whether game theory involves mathematics, the answer is obvious: not only, but also very advanced mathematics. Robert aumann, one of the winners of the 2005 Nobel Prize in Economics, was born in mathematics. Many things he studied were abstract and even impossible to apply. With the development of game theory, some physical methods and concepts are introduced, such as quantum game, which draws lessons from quantum physics and forms a unique paradigm.
Of course, you don't need to study this so deeply. After all, you are a liberal arts student or an elective course. However, from the development history of game theory, it is quite interesting to get to know the background and founders of some theories, such as robert aumann, Nash (the protagonist of the movie A Beautiful Mind) and von Neumann (the pioneer of computers) I just mentioned. Get to know these people, and you will get to know the game theory.
As for the benefits of learning game theory, it is related to the depth and breadth of your study. If you go deeper, you will find a new perspective to study the problem, which may inspire you to look at other problems. If you are shallow, you may not think in this way, but it may also inspire you. For example, the tactics and wits in Romance of the Three Kingdoms are full of game ideas. If you are interested, you can try to explain it with game theory.
That's all, I hope to arouse your interest in learning or provide you with a direction.