So after various comments and questions and the like along these lines, I think it's about time I submit a proper answer for this question.
The first requirement, and an absolute prerequisite for all other requirements is that it is you and not anyone else who defines what masculinity is. For this reason, how it manifests isn't so much based on genre so much as the individual world being portrayed. It also means it cannot be used as a means of weaponized feminine shame and blame, as these have no impact on the truly masculine. Indeed, all emotion based appeals, particularly when used for the purpose of manipulation are summarily, practically automatically discarded by Real Men.
Along the same lines, the terms "Real Men" and "human" can almost be used interchangeably in this context as determining how masculinity should manifest is a matter of thinking and adapting and not merely following some programming script.
Now, take Gerulf (pic related) for instance. If Gerulf behaved on Earth in the exact manner he behaved on a real world, he'd be a supreme fucking cuck and this is explicitly acknowledged at one point. He would be summarily used and discarded by those around him, who would then disavow the very actions he'd taken for their benefit. Obviously, exerting any or all effort on behalf of Earth is the obviously incorrect choice. While Gerulf is not perfect, he is an intelligent, self respecting men and a stand in for my target audience who is the same. He will make mistakes, but not obvious mistakes like this. Indeed, the story begins with him already aware of this problem and being presented with a solution. Leave. Let Clown World die in its dumpster fire. It cannot be saved and does not want saving. Live out the rest of your life on a world that isn't in terminal condition.
Of course, the true red pill is that, at least as far as Earth goes conflict isn't worth engaging in beyond protecting yourself. Play stupid games, win stupid prizes. While this line is usually used in the context of trusting a female and then suffering their sudden yet inevitable betrayal, this isn't a matter of the Thot Question for the simple reason that masculinity is not defined by outside sources and it certainly isn't defined by females. That and, even if zero females are involved, the statement remains true.
Of course, this is fiction, and stories require conflict in order to exist, which means they can do highly unrealistic things like present worlds that are worth saving.
So what happens when Gerulf escapes and quickly enters a new world that meets this criteria? He realizes very quickly the old rules are no longer accurate. The people he meets are not necessarily his enemies and might even be his friends. More than that, the people are people and not NPCs - being residents in a "game" world just adds more levels of hilarious irony. He quickly finds things that had been lacking, some of which he didn't know of and others he could barely comprehend. Things like honesty, loyalty, integrity, love. It was a world where such ideals as Family, Friends, Community were not heretical, but were in fact the natural order of a natural world operating under Natural Law - and they are only noteworthy or remarkable at all because Clown World is so thoroughly unnatural that merely having a culture was enough to induce severe culture shock.
That being said, Gerulf is very adaptive and accepted this new, true reality rather quickly. And then various threats, some familiar and some not began endangering it. At this point, all the trite and predictable answers are perfectly and completely apt. As for whether Gerulf qualifies as a hero, that depends on if you are using the western (read: soy subversive) definition of the term, or the correct one. After all, Gerulf isn't nice. He is however, supremely competent (and works very aggressively to correct any incompetence or other deficiency that should manifest). He is exceptionally devoted, to those who deserve it. Likewise, an exceptionally determined, implacable foe to those who deserve it.
"I said I would get her down, didn't I?"
Anyone who has read my books, and understands the context in which that line was spoken has a very good idea of how far he'd go... for those worthy of such dedication. Some soycattle back on Earth? They remain unchanged and so the correct stance on them remains unchanged. Or, they have chosen to get worse, which reveals that every man, every woman, and every child in this world is perhaps, more masculine than most of Earth...
Meritocracy will do that for you.