Based on the main reasons I use game wikis, these would help solve the problems that players use wikis to solve:
(I'm not saying these things are "bad", necessarily... even if I am a wiki-prone player who'd prefer to have the game tell me things instead of needing to use a wiki. But you're asking how to make a "wiki-less game", so I'm answering that.)
To puzzle or not to puzzle
If you have puzzles of whatever variety in your game, it's practically guaranteed that some players will get stuck on those and look for a solution elsewhere (if possible).
People looking for a solution is just a consequence of having those puzzles in your game, and isn't necessarily a problem. Although it is worth considering how fundamental that puzzle is to the broader game - crowbarring some puzzle into a completely different game might not be the best idea.
To minimise wiki usage, you could offer a "hint" in game, perhaps with some cost. Perhaps there could be a setting to show hints or one to skip puzzles entirely. Players who can't or don't want to solve the puzzle would appreciate that, and it wouldn't affect players who enjoy solving the puzzle.
Of course many puzzles are randomly generated (and there are lots of valid reasons for that, like replayability), and a wiki might not be able to help players with that. But I wouldn't make a puzzle randomly generated just for this reason, because that's trying to solve a problem that isn't a problem.
Don't rely too much on learnt in-game knowledge or memory
(and) Avoid unclear descriptions of items/ability/effects
(especially in roguelikes)
Of course some things are more reasonable to tell a player and some things are more difficult to tell a player. For example, you don't know the attack pattern of every enemy. Or you don't know exactly how some skill will play or how some item will affect gameplay until you've actually used it. This is to be expected. Although some games show you a preview of a skill or weapon, or allow you to try it out before committing to it... which I find useful where appropriate, but that's unrelated to wikis.
Some roguelikes (for example) go beyond the above, and in their item choices (e.g. in shops), they don't give you any item description, either until you actually pick up the item for the first time, or they just never show item descriptions in item choices. Some go even further and never show descriptions period. Those are the games where I'm alt-tabbing to a wiki every few minutes.
If you play a game a lot, you know what most of the items do, so a lack of descriptions is essentially just punishing a lack of knowledge or poor memory, or it's just punishing you for being a new player who hasn't yet unlocked the description by getting the item. So I'm going to use a wiki because I don't like being punished for that.
On a similar note, games might have vague descriptions (e.g. increases your damage "a bit"), so I might head to a wiki to get some more specificity there (e.g. the actual percentage damage increase). It might have poorly explained (or unexplained) status effects. There might be poorly described stage options on a stage selector. Etc.
Don't give choices with unexpected or unclear outcomes
For games with dialogue options, I tend to have a wiki open all the time to check what effects every single one of those choices would have, because I don't want to end up with some inferior story or reward because I bet on the wrong dice roll. I'm probably not the "intended audience" for games where player choice is commonly intended to have far-reaching consequences, and it's probably expected that I'd use a wiki for such games.
Although it could help to give players some idea of what the consequences would be for any given choice. And if a game has a few select cases where there are far-reaching consequences, it might make sense to be a lot more specific about what would happen.
This also applies to choices that seem important to the player (regardless of whether they are important). I remember in Borderlands at one point a character asked if you like their moustache or something, and it said the choice would have permanent consequences. That made it seem important, and I looked it up on a wiki, even though the end result of the choice was just whether the character had a moustache in future scenes.
On the other side of that, some games blindside the player with a seemingly insignificant or unrelated choice that ends up having further-reaching consequences. You might be able to avoid them using a wiki before that by doing this, but you'd annoy them (especially if they can't load to a point before that at all or without losing a lot of progress), and they might get paranoid about the consequences of every single decision for the rest of the game, and possible for other games too.
Another example from Borderlands: most choices only affect the immediate quest rewards with no long-term consequences. In such cases, you could avoid wiki usage by just telling the player what you'd get for each option (a vague "this choice gets you a shotgun" may be enough for some, while others would head to a wiki if given anything short of "here are the exact stats of the shotgun you'd get").
Tell the players what to do and where to go
Sometimes players get stuck, e.g. because they can't find the path forward or because they have no idea what a quest expects them to do. So they check a wiki.
To solve this problem: Make sure that the way forward is always clear (or maybe have some hint or direction marker show up on command or if players take too long). Make sure quests properly describe how to complete them. Sometimes the quest giver tells you what to do, but that's not reflected in the quest journal - don't do that.
Maybe you want a game that's more focused on exploration, in which case you might not want to "hold the player's hand" in the ways described above. But then you might expect players to head to a wiki (which isn't necessarily a problem).
Have (proper) in-game help
If your game has some "help" section, a "codex" or something of that sort, that could help avoid a lot of wiki usage.
Although it also has to work well enough that players prefer using it to using a wiki. That might end up being more work that it's worth.
This could also be better integrated into the game than a wiki, which is a huge potential benefit. Yes, you don't have to alt-tab, which is something, but you can potentially also have clickable links on item or skill descriptions that take players to the in-game help. Although I'd caution against putting everything there as a replacement to having proper descriptions in the default UI (but having it as an addition is fine). If there's a skill that "curses" an enemy, for example, the levels of increasing quality-of-life would be: 1) not telling the player what "curse" does, 2) telling the player what "curse" does somewhere else, 3) linking to that description from the item, and 4) just having that description on shown by default, or as hover-text, on the skill itself.
Players using a wiki is not the problem, it's the symptom (if that)
Note that I didn't say solve the "problem of players using wikis" at the start, because players using wikis is not necessarily a problem in itself. But they do wikis to solve problems that you could help them solve in-game, like those described above.
They might also use wikis to just get more information or trivia about the game and the game world, which might be something you can't or don't want to necessarily solve in-game. Although having a "lore" menu in the game could address some of that.
If you want players to "figure things out themselves", you might have a fundamental conflict with the typical wiki-prone player. In that case, I might suggest that you just don't concern yourself with the possibility that players might use wikis. Players who want to figure things out themselves will do so. Players who don't will use a wiki. If that's what they want to do and what is the most fun for them, there's no reason to design your game in a way to specifically try to stop them from having fun (and you have every reason to not focus on designing your game like that).
There is also a positive element to wikis in that it furthers community-building, which could help the popularity and impact of your game. ... although intentionally making the gaming experience worse so people use wikis will most likely hurt the game more than it helps, because the game needs to be enough fun for people to form a community around it.