Is evolutionary game theory a useful modelling tool? Has evolutionary game theory ever been used to successfully describe an ecosystem or a reasonably closed subsystem of the economy? A frequently used example is about side-blotched lizards but I don't know of any others. And has it ever been proven that in this case the main factor is really relative fitness of strategies and not some other factor, such as the dynamics of gene recombination?
You're looking at it from a particularly biological point of view. I know nothing of side-blotched lizards, but I can say that evolutionary game theory is often used for equilibrium selection. In games with more than one equilibrium (whether it be Nash or otherwise), evolutionary game theory can allow us to select a particular equilibrium that is a better prediction than others in that a population is, in some sense, more likely to reach it and stay there than it is to reach and stay at other equilibria. Have a look at Population Games and Evolutionary Dynamics by William H. Sandholm if you want to see more of how economists use evolutionary game theory. What your question gets at is really more about creating a model with evolution to describe an ecosystem rather than evolutionary game theory, though the two are not unrelated.