A fancy environment full of puzzles involving circles and lines
The Witness is a very unique puzzle game. While it is set in a beautiful environment, the puzzles actually present are often similar and of variable quality. Ultimately, while the game is very innovative in many ways, the beautiful environment tends to distract from the weak puzzle design and non-existent story. Also, there isn't a soundtrack. I thoroughly enjoyed this game, and I think you will too, but the puzzle design isn't as strong as some other games so you may be better off picking up a different puzzle game.
Teaching Puzzles with Puzzles
The most unique part, and biggest strength, of The Witness is the way that new mechanics are taught to the player. While other games may use text to explain mechanics, or show you how it's done, The Witness simply leaves you to do it yourself. You are never told how any of the puzzles work before you actually do them. You are taught how to solve puzzles with... more puzzles. This is a really great approach and was very well implemented. In each area, it would begin with simple puzzles which you could then guess solutions for, eventually working out how each object behaves, allowing you to complete more difficult puzzles. This meant that instead of the game telling you how things work, you have to figure it out yourself, which made learning new things far more interesting. I expect many games to copy this approach.
However, there are some drawbacks. It isn't always clear when you lack the knowledge to solve a given puzzle, so I have spent a significant amount of time trying to solve a puzzle before when actually I did it in the wrong order, making it far more difficult for myself. However, I found things were generally laid out well to avoid this scenario.
Let's talk about the puzzles themselves. Puzzle design is really tricky. I've played a lot of puzzle games, and I always find myself criticising certain puzzles that were unintuitive or too easy. Overall, The Witness feels fairly difficult. There were a few puzzles that I was unable to figure out, however after searching for the answer I often felt like the solution was unsatisfying or the mechanic wasn't well explained. Many of the puzzles were challenging and satisfying to complete, but I'd say there were more than average that were not well designed.
While there are lots of different mechanics, ultimately a lot of the puzzles are fairly similar, all essentially boiling down to "circles and lines". This can make the game start feeling repetitive as, even with different mechanics, you are solving fundamentally quite similar puzzles for 20 hours.
One of the biggest strengths I hear about The Witness is the environmental puzzles. The idea that instead of simply using the puzzle in front of you, you have to look at the surrounding environment to discover the solution. However, I did not like the environmental puzzles. First of all, it was hard to realise that it was an environmental puzzle at all. It's important that puzzle games clearly present what is and isn't part of the puzzle to allow for deductive reasoning to take place, but this was never clear with The Witness. I found myself frustrated when I had to google how to do something only to realise I was looking at it from the wrong angle. Even when I did know they were environmental puzzles, I found discovering the solutions uninteresting. It was essentially "walk around until you find the right angle to make the solution obvious". While some of the puzzles were unique and interesting, many of them were a bit like the "spot the white wall" sections in portal which I did not enjoy.
The Environment & Visuals
The Witness is set in a very pretty environment, which is partly why it's a bit of a shame that most of the game is spent staring at little boards with 2D puzzles involving circles and lines. However, it certainly elevates the experience. The game will also run well on medium to low end hardware as many of the visual effects are not demanding to run but have a lot of style. This does lead everything to look very fake, but this doesn't matter as it gives it a lot of style and makes it very appealing to look at.
Story & Ending
While playing, I was desperate to know more about why I was on the island and what happened, but very little of this was actually answered, at least in the main ending. There were many audio logs which I expected to provide interesting information and backstory to the world but instead gave some pretentious philosophical statements that were often uninteresting. While some people will defend the ending, I found it unsatisfying and not in a way that could seem deliberate with the design of the rest of the game. The puzzles towards the end also had wildly inconsisent difficulty and were often frustrating.
Disclaimer: I have not played beyond the main ending. While I am aware there is 'secret' content which can provide more information, the main ending did not motivate me to continue playing, or make it clear that there was any other ending. I also did not find this content to be very well executed from what I could see on YouTube.
Overall, I have mixed feelings about The Witness. The visuals are superb and the way that new mechanics are taught are genius. But the puzzles were often frustrating or uninteresting and the story was almost non-existent, leaving more to be desired. If you like puzzle games, and particularly games that don't explicitly tell you what to do, then you will probably enjoy this game, but if you haven't played many puzzle games yet I'd recommend some of the others above The Witness.
Other Puzzle Games
A short parody of The Witness that is well designed and well worth playing, particularly if you've played The Witness. It's free!
Baba is You
While difficult, the puzzles were unique and always satisfying to solve. This is the best puzzle design I have ever seen in a game.
While I'd say the puzzle design is average rather than outstanding, the writing is brilliant and the story is also good.
Not nearly as well known as the others, it almost holds up and I think deserves a bit of a shoutout for being a great puzzle design, albeit one that ends a little too soon.