how can kin selection be altruistic?
Part of you confusion is purely semantic.
Kin selection cannot be altruistic. Kin selection is an evolutionary process. Altruism is a behaviour. Saying "kin selection is altruistic" is like saying "natural selection is flying" (when thinking of selection for flying abilities in, say, flying squirrels).
Altruism is a behaviour in which increases another individual fitness at the expense of its own fitness. However, this definition lead to confusion of whether one is talking to lifetime fitness or only to a contribution to one's fitness that will eventually be returned. For this reason people talk about True Altruism and False Altruism
True altruism is a behaviour in which the actors's (the one performing the altruistic behaviour) life time fitness is decreased while the recipient (the one benefitting from the altruistic behaviour) is increased.
True Altruism can only evolve via kin selection (or group selection for the few who still view these two processes as different).
It is the indirect component of the inclusive fitness that selects for altruism indeed.
False altruism refers to cases where the actor performs the behaviour because he is expecting (not necessarily consciously) a return later in life. False altruism can be seen as an investment.
Such false altruism can be selected by natural selection (no need to consider indirect fitness). "Return on investment" can be caused by direct reciprocity or indirect reciprocity. In case of indirect reciprocity, some populations can use a system of reputation, where individuals are more likely to help individuals that they have seen being helpful to others before.
All types of interaction between individuals can be modelled in game theory. One can also investigate specific type of strategy in response to a a specific game. For example, Tit-for-Tat is one type of strategy in a multiple encounter between two individuals game.