The fact that only male individuals presents the disorder can be a strong indicative that it is sex-linked. However, it is important to understand the inheritance pattern.
In the second generation, females passed it on to males, but males did not passed it on to females. This suggests that the disorder is X-linked, because males has only one X and they always receive it from the mother. Also, males never give an X to males, because the only Y that males have always comes from the father.
But male parents also give an X to daughters, and this is where we can tell that it is a recessive disorder. Why wouldn't the daughters have it if the father has it on its X chromosome and he surely passed it on to the daughters? Because, as it is a recessive disorder, the females would need two X's with the allele for the disorder in order to present. But males has only one X, therefore they will present it because there won't be any dominant allele to supress it.