Perhaps not on the same level as TSS, but it's also not really trying to be. TSS builds on a skillset developed over multiple earlier games in the series, and quite honestly, isn't really approachable on its own to a DROD outsider.
The Witness, on the other hand, teaches you how to play itself using its own systems, with the exception of the prompts in the starting tunnel for how to move and what to press to interact with the panels. It assumes you're coming in with no prior knowledge of how to play the game, and lets you figure out how its systems work on your own. It's much more about the 'Aha!' moment than any other game I've played in recent years.
That said, TSS does story far better. It did perhaps bother me a little bit that the entire actual story of The Witness, what story there was, was hidden in the two secret areas, and not once made an appearance in the easily-accessed parts of the map.
I didn't really mind the timed puzzles, though. The one in the jungle was less a timed puzzle than an indication that I was missing something about the systems in that part of the map, and the post-game one was positioned as more of a 'prove your complete mastery of the game concepts' than anything else. Yes, it was a little obnoxious at first, but I found it to be a fun challenge at the end, especially once I had the 'aha' moment about it.
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Caravel Official Holds Progress:
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×KDD 2.0: Mastered!
JtRH: Mastered!
The Choice: Mastered!
Perfection: Mastered!
Halph has a Bad Day: Mastered!
Beethro & the Secret Society: Mastered!
Beethro's Teacher: Mastered!
Smitemastery 101: Mastered!
Master Locks: Mastered!
Master Locks Expert: Mastered!
TCB: Mastered!
DDDoD: Mastered!
Tendry's Tale: Homeland
Complex Complex: Stuck on the first puzzle
floor.
Suit Pursuit: Mastered!
Finding the First Truth: Mastered!
Gunthro and the Epic Blunder: Mastered!
Flood Warning: Mastered!
The Second Sky: Perfected!