The things in AW are just props. All of the story is about who the characters are and what they want. All of this is put under pressure by what what they need.
AW isn't about does that enemy have enough HP / damage / threat to challenge the party. Really AW doesn't even have a party. Your characters are just as likely to butt egos against each other and make that interesting, as butt into the world they're struggling in. If you have a big fight in AW, the fight is just the tip of the iceberg. What is underwater is what does this fight mean for the environment? Who lost family, who was wronged, who gained, who took more then they should, who in the heat of the moment did something unforgivable, who gained from the fight, what is now vulnerable after the deaths, how are either side dealing with the fallout, what is no longer guarded? In AW things rent black and white, if that guy you just killed ran an entire gang, that's a lot of chaos you just introduced into the world. Maybe he was holding back some other evil, maybe he was subjugating some religious fanatics, maybe he was supporting a larger picture you didnt even see, maybe his brother was someone doing something good for the world, but now cant, or now is distracted by you, or whatever.
AW is about all the rest that happens. It's not so much an adventure as it is a story about people. Which can be an adventure if the person is adventurous.
In D&D you might reward a fighter after an epic battle with some magic sword of all this coolness. In AW, even if they find some kick-ass weapon, it's just dressing, flavor, the real importance is how the ego of the players butts against the egos of the world, and what they try to do about it. One of my players wanted something really scare powerful, and they were already touting around dangerous weaponry, I told them what they'd have to do to get it, and they did, they pulled it off. So they got the crazy cool thing, and used it to frighten people, it had the tags terrifying, wrong and had an additional vulnerability backlash. We just described it as doing more then killing the person, it ripped their ghost into spreads (meaningful in the given apocalypse). Backlash could mean socially, morally, spiritually, or physically. It ended up rupturing the characters psyche, he lost what was real and he had full hallucinatory conversations with people that were long dead, or overlayed people from the past on people now. The player bloomed, and he drove almost all the coolest events, I just dropped generic prompts now and then, and he ended up pushing weird all over the place.
Definitely not your traditional here's a +5 weapon.
In a word, playing an adventure like D&D in AW is hard, to impossible, and you definitely should not try to house rule it in on your first game or two. If you want something that's halfway this and halfway that, InverseWorld and DungeonWorld are both structured in that vein.