The short explanation is that, unlike most open world games, it is a cleanly designed game with excellent base mechanics. Every mechanic is important to the core gameplay loop, and feeds into everything from combat to exploration.
Furthermore, the mechanics are all very simple.
You have health, stamina, a temperature gauge, and breakable weapons. And you can go virtually anywhere as long as your health, stamina, and temperature allow you to (and you have a decent weapon to defend yourself).
- You can go fight the final boss right after the tutorial area -- but pretty much everything is going to one hit you (so you need to become more powerful) and the axe you get in front of the first fire isn't going to cut it.
- You can go to the volcano right from the start, but you'll die from heat (and will need to farm some special items to survive the heat OR do the quest to get the heat armor).
- You can climb any mountain you want but might freeze to death at the top (so you'll need to constantly start fires / carry a torch / eat hot peppers / find some warm clothing).
While some of the mechanics can be likened to Ubisoft (climbing towers to open the map) -- BOTW does it SO much better because of it's game design and mechanics. In a Ubisoft game, every tower / outpost is exactly the same. The challenges are the same. The enemies are the same. They all blend together and become repetitive tasks.
In BOTW, however, even the simple things like towers are all slightly different. Some of them are only accessible by climbing mountains and navigating through storms. Some are closed off with vines that you need to clear. Some are too tall to climb on your base stamina (without some stamina food, that is). Some are protected by enemies that will snipe you from a mile away. None of them are exactly the same, but all of them are accessible if you just take a second to think your obstacle through.
And all of this minute to minute experience is bolstered by amazing mechanics and design:
1. Excellent traversal mechanics
- Go anywhere and climb anything
- Shoot up and glide to quickly get around
- Stamina system makes climbing and gliding actually rewarding (as opposed to spamming the jump button)
2. Rewarding exploration
- Spotting and tracking down new shrines
- Unique, fun trials scattered across the map
- Literally hundreds of korok seeds hidden through the world with fun little puzzles
- Dozens of secret areas, cracked walls, etc.
- Difficult, unique enemies hiding in far-off / difficult to reach places
3. Logical and fun game physics
- Grass? Trees? I should be able to cut that... whoa!
- Explosive barrels? I'll just hold my arrow over a fire and... whoa!
- A raft with a sail? I wonder if I can use my korok leaf to propel it... whoa!
- Lighting hitting everything around me? Unequip your metal equipment... whoa!
- Freezing in the mountains? A torch should be able to warm me up... whoa!
- Shit, out of arrows. I should be able to use magnesis to wallop the enemy... whoa!
- It's raining in the middle of a battle? Would be cool if I could use my shock arrows to kill everything... whoa!
- Ice blocking my path? I wonder if I can use my torch here... whoa!
Again, the mechanics are very simple, but everything works together so well and acts to build more immersion and cohesiveness to the experience. It's not a bunch of random mechanics that turn into their own separate mini-games. Everything is about how you interact with the world and environment, and you're never taken out of the experience.
If you compare this to any other open world game with a critical eye, you'll realize that these so-called "basic" and "logical" mechanics are missing from all other open world games.
Sure, Assassin's Creed lets you climb. But you can't climb everything, you're constantly blocked by invisible walls, and there's absolutely nothing rewarding about holding a button to parkour and scale a wall after the first 5 minutes of gameplay. There's no sense of accomplishment at all. The simple introduction of a well-designed stamina mechanic changes a boring, rote skill like wall climbing to something that's rewarding and fun.
Sure, you can go /mostly/ anywhere in games like Skyrim and Fallout, but spamming jump at a weird angle to get up a mountain feels janky -- not fun.
And outside of Half-Life 2 and Portal, there are nearly no games that use physics to the same satisfying extent as BOTW. And certainly not open-world games, which tend to have absolutely laughable physics.