Solarus is a free and open-source game engine, licensed under GPL v3. It is written from scratch in C++ and uses SDL2. Consequently, it is compatible with a large set of platforms. You can explore the source code if you're curious.
The goal of the engine is to allow people to create their own Action-RPG games (also called Zelda-like games). It is totally independent from Nintendo, and will be free forever.
The engine itself does not contain any copyrighted code or assets: it is 100% free and open-source. Thus, Solarus cannot be eligible for a DMCA from anyone, including Nintendo.
Solarus currently only support 2D graphics. However, your game does not have to look like a 16-bit game: artstyle is totally up to the developer, and OpenGL shaders can be used to get a modern feel.
Solarus is not an Super Nintendo™ emulator, neither a The Legend of Zelda: A Link To the Past™ ROM hack.
Solarus is not a "Zelda engine" as it can be read sometimes; it can power any Action-RPG or Action-Adventure game (or any kind of game you want, with a little more work). A Link To The Past assets (tilesets, sprites, musics, etc.) are totally separated from the engine (the engine does not contain them).
However, it would be lying to deny Zelda had a great influence on Solarus, because historically it was first designed as an engine to power a Zelda game.
Also, Solarus does not currently allow you to create a game without coding, unlike RPG Maker. In practice, it means you can create maps and sprites with the mouse, but you'll have to code scripts in Lua to manage the game logic and events: trigger a door opening, or give the hero a new weapon for instance. Fortunately, Lua is a simple language and should not frighten people who've never coded. It's a great way to start and learn.
Solarus is a very lightweight engine, and is very easy to develop with.
The engine is very-much oriented towards Action-RPG or Action-Adventure games. The Lua API already contains lots of tools used to build this kind of games: maps, items, enemies, treasures, etc. Using Solarus for that kind of game will greatly reduce your development time. In Solarus' jargon, games are called quests.
Solarus provides tools for game developers and players:
Solarus offers a Lua API, so all your game's code can be done in Lua. The C++ engine will take car of all heavy computation (graphics, collisions, etc.), and you'll just have to write the game's logic. In theory, you shouldn't have to dig into the C++ code. Which makes Solarus a good tool to start learning how to code. Still, Lua is a powerful language that is widely used in the video game industry because, in spite of its apparent simplicity, it is very powerful.