If you try to visualize (or even calculate) the number of possibilities given every possible variation as Jostenmeat mentions then the answer to the question 'Will we ever run out of new music' is most definitley NO.
But, the way agarwalro summed it up is what I got out of the video. Even if you narrow the problem space considerably by imposing a lot of restrictions the number of possibilities is still enormous...but then why do we continue to see (hear) 'new' music that very closely mimics what has come before?
I thought it was pretty interesting in the video where he played that 'dance' type song and then went right into 'Cecelia' by Simon and Garfunkel and it didn't miss a beat...like it was the same song with different lyrics.
Given that the possible number of combinations is enormous regardless of whether you narrow the range by imposing restrictions or take into account every possibility as Jostenmeat does, why do human beings reinvent the wheel (musically) time and time again?
I think the answer to all of your questions is easy, and is two-fold: 1) They are simply ripping each other off. 2) The subject IMO is more about popular music, and how it sounds similar, and I mentioned that I think this is what the title should have been, as it does a better job of that than talking about musical possibilities. IOW, I do NOT think we are constantly reinventing the wheel. But I think POP music writers might!
Let me throw out some other points as they come to me (besides number of notes, or octave range for instance), some I may have touched upon, some maybe I haven't, that all point to greater complexity in (Western European) music; stuff that just blows past the "restrictions". Some are more salient than others, and they may be posed more as questions.
1. Has anyone ever, ever heard two improvisations that sounded exactly alike? You're allowed to use the same musician too! I probably have some jazz cds are around, with some "B sides", and the improv is never the same, even if they all begin with the same chart.
2. Did you know that you could give two composers the exact same melody, and when they write parts for it, even when using the same "writing language", such as common practice period writing (the stuff you learn in 1st semester harmony/part-writing), you can get totally different music! (Pop music doesn't really use "counterpoint", which is one of the greatest, and IMO the greatest, feature of our Western European music, and instead they play a simply chord vertically, and repeat that same simple chord over and over again.) Yes, so say the composers are given the same melody for the soprano line, but the alto/tenor/bass might all be playing different notes during the entire passage. Now, give them freedom of "writing language" as well to boot, and then the treatment becomes even more dramatically different. The "melody" is on top, but instead we can use any of the SATB lines; give one of those being exactly the same to two composers, and the end results can come out very differently.
3. Then the video's bit about 4 chords. This is another reason why "all popular music sounds the same". They all sit on the same chord for many bars at a time. The chords that are of the most possibly simplistic type you can possibly choose out of all the chords we would be allowed to choose, even using writing languages that are hundreds of years old. The guy whose work is the foundation for any first year part-writing book you'll pick up from the shelves (Bach) has a much more intense "harmonic rhythm". (He didn't think of it as chords, which is thinking vertically; we do that to make it simpler for ourselves; he thought horizontally.) Whereas a pop musician needs many bars for one chord, a composer like Bach would need many chords just for one bar! These "chords" can be sooooooo way more complex too! A beginner slowly learning a work of his, trudging along reading notes "vertically" playing them all the same time, will undoubtedly exclaim, "that can't be right, this has GOT to be a typo", because of the extremely savory dissonances that are had. And this guy is the original gangsta!
4. The paragraph above is more about harmonic treatment of the same idea ("reinventing the wheel" doesn't do justice IMO), but there are other ways you can treat, slice and dice, fry and bake, salt and pepper (or in musico-terms, augmentation, diminution, harmonic treatment, part writing, textural, registers, you name it). That video's bit about Twinkle Twinkle Little Star, that is an old English lullaby, you know for kids, easy to remember, help them learn the alphabet, maybe it's for Baa Baa Black Sheep to help count sheep to go to sleep, I have no idea. But this is what Mozart can do with it!
5. Also in the video, another EXTREMELY limiting restriction is the use of melodies strictly from an 8 note scale. Did you know the greatest composers you've ever heard of from the LAST century were normally using 12 note scales? Like Stravinsky, Schoenberg, etc? Now, depending on the work you pick, undoubtedly some people here might have hard time calling it music. But it's not because it uses 12 note scales to derive their "melody". Heck you can be forced to use ALL 12 of them for your material, and still have very beautiful music that IMO is still easy on the ears. The below is an example of such, I really enjoy this work.