I'll add my 50c (sorry for longer post)
Replayability is often tied with whether the game is story-driven, multiplayer-focused, simulators or sandbox (etc. but let's describe this categories):
Sandbox games are clearly one of the easier to be replayable - while the progress is often similar in all runs, it is creative after all. Each run will likely be different (if you combine it with multiplayer - like Minecraft or Factorio). This being said though, these games tend to be somewhat hard to design in a good way. After success of Minecraft, many other sandbox (or semi-sandbox) games appeared. Pretty much every major title (with few exceptions) has added crafting, base building, etc. Thinking that it would add to replayability. And … well … it did NOT.
Multiplayer-focused games are clearly replayability focused. Games like Counter-Strike, or modern Hunt: Showdown … or even massive multiplayer ones. These are focused on replayability - designing these needs to have highly polished mechanics of the game and community part of game.
Simulators are a bit of … well, different in this case. With them you often focus on specific group - like train simulators - the group isn't that big, but is willing to extremely invest into them. They also require very hard level of details in how given thing works, and high interactivity level (simulation issues being the worst - which is why KSP 2 is often viewed as absolute failure). Replayability here is quite clear - simulation in various situations, if those can be user-defined (editor), replayability becomes literally infinitely long.
Story-driven games are extremely hard to be replayable. As I enjoy them very much - replaying a story-driven game is boring. Going through new Tomb Raiders is enjoyable first time. Every other time it is boring - collectibles doesn't help that much (when you look at Steam achievements, it is clear why). Large RPGs have also similar problem (Witcher 3 and their re-release) … same thing with Horizon: Zero Dawn. These games are quite linear. Character development is also not that free (you can't really make an “archer/ranger Geralt” or "Aloy with medieval warhammer” (and if those studios do it, I want credits)). Jokes aside - is there any story-driven game that is replayable? Yes. And it's old Gothic 2.
Why? Because it does allow you quite massive customization of the character that develops (multiple completely different routes), and while the story changes very slightly, many missions change completely (you are literally having completely different series of quests based on how you choose). Also, many of the quests/tasks have multiple ways to finish. They did attempt it in Gothic 1, which did work to some extent, and perfected in Gothic 2. Let me state example:
At the beginning of the game, your task is to get to the city - which is a harbor town. And because you're in torn clothes, looking like a former convict - gate guards clearly doesn't allow you in. There are multiple ways to do that:
- Obtain farmer's clothes and state that you are a farmer going to the city (which can be done in multiple ways)
- Buy clothes from the farmer
- Steal clothes from the farmer (he will know that in future!)
- Work for the farmer to get clothes cheaper
- Obtain city-pass, which proves you are a citizen (at which point they don't care how you look like)
- You can receive that one from trader for a “help in future” (of course it's something shady!)
- Note: In future if you get him imprisoned, gate pass will be void and you're not allowed to the city anymore
- Bribe the guard
- Get over the wall (this is a tricky one - requires proper position, jumping, etc. … it will still award you the experience, so authors took this into account)
- Go around the city, jump into the water, swim around to docks and get out of water there
- One could state that this one is an exploit. It isn't. There is a guy from first game, who remembers you, and laughs that you'd do anything to get into the city
It's a single quest - yet impacts others in future and there are several other quests that can impact it. With such design (true) replayability can be introduced into story driven games - not just “collect 500 stars”, which is mainly boring and annoying. Of course, designing such quest lines is somewhat hard, as introducing any paradox or problem into the story breaks immersion.