I think everything you can find on the witness is intentional and ends up in a net positive. Yes, even the seemingly random videos, and even the environmental puzzle that has you wait a full hour while he mocks you in the background that you're only doing so in order to collect everything. So even if something feels like a bit of a stretch in this, I'll try to explain it or I think it's deeply based on world building.
There are two 'halves' regarding The Witness' story. One is about you - as someone new to the island. It doesn't matter what your identity is, however - what it matters is what you go through, the places you see and the things you do. What matters is the events that you see unfold. You're literally your own witness to your own journey and the things around you, and I don't think the title was chosen for being a 'catchy word with impact'. But what exactly are you witnessing? Well - this ties directly into the two halves. You're witnessing first hand your own process of learning and discovery. You're learning new languages, learning shortcuts, beginning to know the ins and outs of the island... I think this also ties with how the puzzles are presented to you - your only weapon is knowledge, and your assumptions, and the world won't mold to your assumptions - you have to see the world for what it is and keep reacting around it.
And the second half is about creation, and the creator of the island - which I think is fair to say, it's about Blow. I know it sounds a bit narcisistic, but I think a 'self-insertion' works well at times, like all the confusion surrounding 'The Beginner's Guide'. Talking about creation, I think it works so well because it doubles as a creation of the island, and of the actual game. The mountain was a factory where new ideas were made, iterated upon, revised, and discarded. Things begin to get a little bit glitchy, off-set. You are introduced to a lot of new concepts in rapid-fire sucession, only for them not to be touched that much later on. You can also see that in the statues of the island - on the outside, even if there are statues of thieves and things like that, you still get very much the picture of a live world, with people living, friends being friends and enemies being enemies - but as you begin to go up the mountain, where gadgets are being set-up, there are people arguing despite making the trek together, and as you go down, you can see the workshops getting more and more messy, until you end on the 'red cave', where a single 'creator' stands over a panel trying to tie everything together. Now this is not my analogy but I agree when I saw someone say it can be compared to Development Hell - near the end, deadlines approaching (everyone got 'statued' in the middle of setting up everything).
And in the end, we have the 'sea'. A sense of serenity, with puzzles still being hard, but something that shows us that everything was done. It paid off. You are asked, as a player, to apply all of your knowledge (besides the ones discarded in the factory hell) in one last challenge. Before going back to the start. Time to begin a new journey, learn new things, see what you accomplished, start anew. It doesn't matter who you are, what matters is that our experiences, what we learned and how we adapted to our assumptions being denied, and how we interpreted everything around us - THAT is what makes us important, unique as a person, and what makes everything have been worth. Maybe things aren't at face value. Maybe you'll be tricked. But that's up to us to discover.
And I think one of the biggest discoveries (and also support for this 'interpretation'I think it's clear that the island was 'created'. Not in a sense of 'here's something artificial', but in a sense of an actual company setting out to make something. We can see this not only be the many couches and pillows scattered through apparently no reason, but also because you can always see a sort of a 'sun' motif throughout the island. The gate right at the beginning, there's some perfume bottles scattered, there's even calling cards around and that is not even going into the developer's ending which multiply the whole thing by a thousand, even if it's a bit weird.
Yes, I do feel sometimes the game feels to pretentious (like the chanting of words in the end, some of the audio logs...), but overall I think it makes for a very cohesive experience - and in the end, what matters is that I witnessed such things and that I made that interpretation - my point of view on everything is what gives the experience value. I don't think it's a cop-out to say that ok, maybe there are other valid explanations for the actual story, and it is a bit too abstract, but I think the whole idea behind the learning and discovery process stands and that's part of the beauty of it.