There is general two conflicting answer to that last question. One is that the effect is very minor and testosterone make certain behavior more likely to occur if and only if specific environment is present. It is very possible that testosterone effect on sex-typical play is dependent if it is the father or mother playing with the child. In addition such experiments in recent time has undergone a lot of methodology criticism. In new studies on primates they found that testosterone secretion is increased after physical fights among males which correlate to how much they fight. Behavior in this case causes high testosterone levels, rather than high testosterone level causing behavior.

The other answer is that practically every behavior is influenced by a combination of hormones, genes, and environment. Everything from athletic skills, obesity, teeth health, stress, sleep, diet, honesty, politics, and so on. To quote a profession, free will likely do not exist and is only the result of all the different biological systems interacting with each other, the environment, and random chance.