Source: Robert Leonard, Von Neumann, Morgenstern and the Creation of Game Theory, p. 9

Often, chess is credited with rather interesting developments in other fields. This is sometimes done by people who are not particularly good at chess, but it is interesting to note that it is also done by serious researchers, as in this case, about the history of von Neumann, the well-known mathematician. The author dedicates an entire chapter to the effect of chess on the intellectual scene of von Neumann's youth - 1920s Hungary - and credits it with much intellectual stimulation of Jews in Hungary in general and von Neumann in particular. 

It is claimed that Emmanuel Lasker's Kampf (Struggle) - his philosophical thesis - was highly influential, indirectly, in developing game theory. Lasker attempted to generalize the struggles in the game of chess to decision-making in life, and used terms later used by game theorists - "domination" and "equilibrium" for example - to argue that, like chess, in life too the seemingly near-infinite number of possible strategies does not preclude finding out, by logical thinking, the best or at least the few reasonable strategies (Leonard, p. 13).

This, claims Leonard, raising the possibility - later examined by Zermelo, who knew Lasker - of a completely objective analysis of chess, for example, mathematically defining a "winning position" by looking at the existence of a set of future moves that allow the player to mate no matter what the opponent does (Leonard, p. 17). Zermelo's paper was the first time (1912) that winning in chess was defined purely formally. From there, claims Leonard, it is not surprising that the idea of a general game theory along similar formal, purely mathematical principles for life, not just for chess, would occur to von Neumann.

I am somewhat skeptical, not of Zermelo's pioneering work, which very likely influenced von Neumann, but whether Lasker's Kampf was of such great influence on Zermelo. After all, one need not read Lasker's philosophical works to know Lasker, be interested in chess, and attempt to describe it mathematically. I am not convinced that it was Lasker's Kampf that gave to Zermelo, or von Neumann, the idea of the possible analogy between chess and life that led to game theory.