Sorry but that is simply not the case. Read John Maynard Smith's works dealing with game theory and ESS.
References please.
References please.
Do remember that altruism is not expected in all cases, but then neither is bloody tooth and fang style competition, it is a continuum that is a function of the genotype, phenotype and niche space.


A brief overview.
Introduction to Smith’s ‘Evolution and the Theory of Games’ (1)
I like how Smith acknowledges that much of this is speculative, philosophical, cannot be tested, and has challenges.
I'd like to reason about those challenges. I'd also like to acknowledge that I find a lot of this intriguing, as there is no doubt a "game" and altruism in the reality of life.
Altruism is a behaviour whereby an organism acts in a manner that temporarily reduces its own fitness while increasing another organism's fitness, with the expectation that the other organism will act in a similar manner at a later time. (Tit for tat-reciprocal altruism.) However, can this be viewed as altruism? It is selfish when an organism does something with expectation of something in return. Wouldn't that be considered vain? So it still, simply is the case and not the case based upon how altruism is defined and used. Cooperation/altruism is being viewed as selfishness. How would an organism predict/know/have expectation that they'd be taken care of at a future time? This is blind faith being incorporated with ESS/game theory.
The transfer of information during contests, Smith acknowledges as his biggest concern. The initial, being.. how did these rules evolve? What/who makes the rules? It's easy to say that genes are very powerful and do all of the work, but genes are useless without an organism/self/individual making them useful. Acting upon, understanding, and performing the transfer of information. Essentially, a shaper and executor of the information. It requires that an organism be capable of assessing the degree of relatedness to an individual before acting resulting in concepts that must extend beyond the immediate genetic relationship to include other organisms where future genetic exchange may occur, including environment. This is not to mention, that an individual/self is always and gradually changing its own innate genetic constitution in correlation with the base of genetic constitution that cannot be altered/changed. This also applies to information in genetics, what/who wrote this information? Did it accidentally program/write itself? Is it an innate/built in mechanism mirroring itself?
When I also try and look into inclusive fitness examples.... there are only "some." I also find that in reality, this is not always the case amongst the wide array of diversity. It would seem as a shortcut is being taken. That since there are a few examples in certain species, they "demand" that it must be for all species.
Game theory and ESS are interesting perspectives, and not wrong. However, it does not fully describe the world that we see. (Or at least not all of us.) It describes within limitations, and small portions of reality. It predicts that cooperation should be rare in nature, when in fact we find cooperation wherever we look, and not just among kin.
You also asked for references, but they are visible all around you. Also, the measure of what constitutes "relatedness" is of a large dispute amongst "biologists." I can say that many on this thread are a group, not related in kin, and are fighting for the survival of ideologies(certain aspects of evolutionary theory). Even you and I, not related in kin, and share disagreement on many aspects, can cooperate. This is also highly evident in nature, genetic variance as well as different species cooperating.
I'm not sure when they say altruism started to evolve, but altruism would have been clearly evident given what they also say about the earliest forms of life, undergoing environmental change. Therefore, altruism was there from the very start of life.
