Yes, absolutely. Game theory says nothing about what players want, or what they ultimately care about. It only says how they (collectively) behave given what they want.

It is perfectly reasonable for people to care about others' well-being or wealth in addition to (or instead of) their own---not for strategic reasons but just because they care. Such preferences are an input into a game-theoretic analysis; the output will then tell you how people who have those preferences will behave.

When we write down simple games, we often write down payoffs in, say, dollars, and assume that players value the dollars they get and nothing else. But that is just doing game theory with the assumption that players are non-altruistic. It is perfectly possible to do game theory with the alternative assumption of altruistic or social preferences. See, for one example among many, this paper by Fehr and Schmidt.

There are some game-theoretic models in which selfish agents behave in apparently altruistic ways, in order to serve their selfish interests (e.g., obtaining good future outcomes). I wouldn't call that a game-theoretic analysis of altruism; it's a game-theoretic analysis of cooperation by non-altruistic agents.