Hard Wired Island is a game about community, being economically burdened, and framing your narrative around missions.
Let's talk about how to hack it into something different.
Let's talk Dungeon Fantasy
The most baseline possible example genre is a good one to talk about. Let's say you want to hack HWI into something like that. Putting aside needing to rewrite all the occupations, assets, actions etc. into that (and how I'd mod the combat engine for this), we need to understand the thematic underpinnings and start there.
Community; This one turns out is easy. If we simply keep the rule as is, we can reframe it as A local township. You can go a step further; you can't access some services unless you know a local person who can give you that service, for example certain assets can't be accessed without a blacksmith. This becomes about building a community you venture forth from, or at the least becoming entangled in one. This can recall building a town on top of a dungeon (Dungeon Meshi) or creating your own kingdom (Meikyuu Kingdom, Rules Cyclopedia D&D.) Threats to this community become even more tangible.
Missions; These don't fit as is to your "dungeon fantasy" experience. However, we can reframe these as Expeditions or Dives. I prefer the first for a couple of reason; A Dive would be about only dungeon dives, whereas an Expedition can also encourage you to think about things like extended overland travel, exploration and so on. "Prep" becomes about tangible commodities like potion refills, rations, dungeon gear and equipment, and so on. You'd set off on an expedition by planning one in advance and gathering all the resources, much like missions. Resting might be a one-roll way to get Personal prep, but not the Group prep - regaining spells, VS making sure you set off from your community with enough rope. There might be some thematic restrictions around what type of prep can be spent on what, and some characters (say, Rangers) could significantly be about maintaining Group prep in a significant way.
Burden; Here's the one where there is no one clear answer. D&D, fundamentally, does not have a singular thematic underpinning you can pinpoint; it has a confusing mixture of the author's original ideas and ideology, the expectations of younger and older playerbases, and various elements leaned into or away from to please aging racists who haven't played in 20 years but write blogs that make them seem important to D&Ds writers for some daft reason.
Anyway.
Burden is a thematic underpinning, a motivator, a reminder of why you are fighting, a limiter on a certain type of character resource, a symbol for oppression. It's doing a lot. And there isn't a singular identifiable thing like it that underpins dungeon fantasy. Let's talk our options.
1. You could make it represent something like Duty. Maybe you have a literal knightly duty; maybe you merely have a strong sense of one. In that case, it would be a different kind of mechanic, where you voluntarily take on Duty but must fulfil Responsibilities in exchange for whatever benefit Duty brings and what it means to renege on that.
2. Maybe you have something like Fate. The more heroics you perform or magic you encounter, the darker your Fate is. Your Fate means you are drawn to heroics because it brings some kind of better ability to fight the darkness, but it also inextricably leads to your doom. What does "reducing your Fate" even look like? Certainly nothing to do with Cash.
3. Malignance, Corruption, etc. Maybe you just become more tainted with dark chaotic energies inherent to the dangerous places of your world, old world Warhammer style. You gain this stat and maybe roll random abilities, mutations, etc. And the downside would be related to becoming alienated from your Community.
4. Magic. Maybe interacting with magic at all is a burden. The deals you make, the control you must exert over so much as a single magic sword, the pacts and promises that bind you. You increase your Magic stat to become better at magic - maybe it even acts like a Specialty for casting magic or using artifacts! - but the more you have, the more likely you are to suffer for it. Maybe a Critical roll for magic (succeed or fail) means you add your Magic stat to that critical and if it's 7 or higher, weird shit happens around you. Again, maybe it impacts your standing in a Community.
There's nothing to say that a fantasy version of the game couldn't have all of the above as optional rules, and you simply pick whichever is most appropriate for a given game. Or maybe different characters can have different ones. Or maybe the game has multiple settings and each one explores a different idea! Regardless, the possibilities loom large, but also reveal to us the limitations of some of our most popular games on the market and how they deliberately eschew this kind of thematic focus as much as possible to appeal to "everyone."
In Conclusion
Missions are about structure and flow of play, Burden is about theme, and Community is about tying your character to the world in a concrete way. Understand those elements, and you'll understand how to make the game into anything.
And if you'd love to see an actual in print version of me doing exactly this? Well, make sure to let me know.