I take a more neutral view on this. Master Chief and Kratos are great examples of what could be called "toxic masculinity". They are the epitome of the duty-first, hide-your-emotions male. But they are also great examples of why toxic masculinity is a flawed concept.

Both of these characters have lived lives where discipline and emotional control were key to their survival. They have learned resilience through hardship not by taking the female approach to emotion resolution, but by taking the male approach. Instead of letting their emotions out by crying and socializing, they channeled them into their work.

There is a time and place for both methods. Neither is inherently wrong or unhealthy. But the latter is traditionally masculine, and would definitely qualify as toxic masculinity by the common definition.