I think you're working with a valid 'question' or 'issue', but I, personally, have an issue with part of your question, and my answer here can be seen as part answer and part (useful) questions to ask yourself about what your actual issue or question is. I begin with the latter.
The Incel
Now, a lot of people reading this question (or anything else involving the term 'incel') may intuitively know what is being referred to. For some readers, their understanding of 'an incel' alligns with yours, but for others it might not. Some may be aware of it being an abbreviation of or originating in 'involuntary celibacy' - others (perhaps younger people) may not.
Something I find jarring whenever anyone uses the word, is when they seem to work from an understanding that this is just the way that some people are, and we should hate them for being like this.
I understand that the term incel is associated with all sorts of troubling (illegal, immoral, destructive) behavior, and my point is never to excuse this/that behavior.
What I always emphasize, however, is the very real probability (if you understand human development and behavior), that these so called incels are the sad product of (a) certain environment(s), either on a local or societal cultural level or indirectly through consumption of various types of (global) media etc - most likely a combination of the two.
I'm aware that the term has slightly changed meaning towards referring to "some sad man who hates women and 'men who succeed with women' and the world - and who, then act atrociously", but this doesn't change much about what could be referred to as 'the approach'.
Now, I could go on about various tendencies, trends, movements, liberations and developments in gender-roles (and other societal factors) and how it has left some (many), especially 'men', lost when it comes to living up to ideals - or confused about what these even are. My point, however, is that anyone who solely focuses on a person being an incel, does more damage than they do anyone a favor. Simplifying or reducing someone to 'an incel' is, to me, a destructive act, because it somewhat takes away their humanness. I wanna emphasize, again, that they (the 'incels') may very well do inhumane acts, and that these shouldn't be allowed or excused, but I would highly suggest anyone using such a term, to consider the difficulty of being a human in a world as complex and demanding as ours, especially if one such human doesn't seem to succeed in things that make them feel like they are succeeding or belonging in society.
The scope of bad behavior and the act of humanizing
Now, it seems that you are yourself aware - to some extent - of the humanizing of this otherwise very hatable character. It seems to me, that the approach to humanizing 'bad characters' depends on the type of 'bad' they represent. Please do not takes this too literally, but perhaps you can think of it as sitting somewhere on a scale from 'local' to 'structural' badness.
Local: Some people go through traumatizing, hurtful events and experiences leaving them hateful, aggressive, depressed, hopeless, what-have-you. The more of these experiences a person has, or the more severe these experiences have been, the more likely these people are to act differently towards other people - to the audience, usually, in an unjustified way. They may become very intolerant of people living differently from themselves, of generally struggle to live a fulfilling life. Or, they may 'simply' have a high temper, low patience, lack of trust in relationships or whatever.
Simplified example: Premise; Timmy's father beat him. Result; Now Timmy has a tendency to beat his partner(s).
Structural: Some hurtful experiences are clear to us as individuals and others are more indirect, vague, odd. We as people in a society generally agree that we are all working on improving society, making it a better, more just place. Apart from 'just' and 'right' often differing between individuals, other issues arise from attempts to improve something.
VERY simplified example: Premise; A society has actively worked on countering patriarchal gender roles and tendencies that seemed to leave women with unfair disadvantages or leaving them in unjustifiable relations with partners, and so on. Result; Men now struggle with understanding how to navigate in a society where their actions towards/with women are scrutinized, and lack a clear understanding of 'how to be a real/succesfull man', a struggle leading to many painful and destructive feelings and urges - do they blame women for 'taking the roles of men'? Do they 'get rid of the other men, the ones that they are competing with for the women'?
In either case, local and structural, we often look at a persons experiences/environment in order to understand how they became the way they are. With a locally hurtful environment, the issue or the 'solution' may be clear. Example: Put more ressources into making sure that children are treated well by their parents.
With the structurally hurtful environment, the issues can seem paradoxical and therefore super difficult to 'fix'. Example 1; Go back to old-fashioned gender roles to help men 'know their place' in society? (Probably a clear no), Example 2: Create a public space where men can air their doubts, frustrations, insecurities and general feelings about uncertainties in life, without being shamed for 'not being manly'? (Perhaps? Seems obvious to me, but far from everyone will agree.)
How could you go about including and humanizing 'incels' in your story / game
If you want an audience to understand how someone may act 'like an incel', make it clear, that they are the product of an environment, locally, societally, globally, structurally.
Your goal, then, would most likely not be to simply find the story that explains this man's behavior, but instead to have the audience experience the tendencies in general which might create incels. From this, we, the audience, might actually generally learn something.
Heck, building on top of @motosubatsu's answer, we might actually get the best of both worlds: We might get to live out our forbidden fantasies of disproportional or totally insane violence (or whatever), and at the same time undergo a slight change in how we view the causing factors of such, 'obviously' totally inappropriate or unacceptable, behavior.
How is this answer relevant to this and other questions about writing/structuring stories?
It may seem like this answer is very heavily focused on the use of the term 'incel' - and it is, but I want to clarify that the term could be switched out with many other terms painting a person as 'bad'; racist, homophobic, bigoted, violent maniac, asshole, and so on. What I hope anyone who reads this answer takes away from it is; Beware of how your use of a term may play into 'creating a narrative that fuels the issue that creates the problematic behavior' which you want to highlight or work with - do you think calling or referring to people as 'incels' is helpful or counters the issue? I do not. In many stories, bad people are created from local 'issues', but if we look closely, just as many could be seen as the product of structural ones. As a last reminder, the point is not to excuse the behavior, but to shift the focus onto what may cause it, perhaps to make sure it never happens again.
If you are not up for this, I would advise against having an 'incel' in your story/game, but the choise is of course yours either way.
I take away from the other answers (and comments) that others may feel something like this, but they perhaps either do not know how to put in into words as an answer or do not want to spend the time and energy writing it. They also may not find it an appropriate place to write such a response, but I couldn't not do it.