> I find this a strong statement that's hard to question or refute, or know how one would show that it's somehow anything more than a general feeling that might be shared by lots of people?

Let's divide and conquer:

1. The Youtube poster probably meant pre-dominant instead of "sub-dominant." Pre-dominant chords are a set of possible chords in a particular system of harmony-- called "common practice harmony"-- which essentially kick off the process of "asking a question" in the chord progression. This "common practice period" of music ran roughly the long stretch when Bach, Beethoven, and Brahms wrote music. Composers today can make use of that system if they wish, but as you'll see below Glass isn't doing this. (Digression: "Sub-dominant" refers to one particular chord choice in a given key, and it's not one which appears at the beginning of the Glass piece in the video. Neither is the dominant, at least in the function implied by the poster as "answering" or resolving the tonic. If anything the beginning of the excerpt sounds like a fragment of a descending tetrachord pattern that goes back to the middle ages, but without the final note. I.e., the bass line of Ray Charles' "Hit the road jack" leading up to but not including "no more, no more, no more, no more")

2. Glass' music in the excerpt is cyclic. You hear some 2-against-3 rhythms between the left and right hand for four measures-- the first 2 have the same chord, and the 3rd and 4th measures have different chords. Then you hear it all over again. This sets the basic rhythm and phrase structure for the entire excerpt-- everything cycles back around in predictable groups of 4 measures each, with the chords changing roughly every measure. Finally, each new phrase starts back at the same, predictable f-minor chord that began the entire excerpt.

3. The voicing of the chords remains in the same small range for the first half of the excerpt. You can play it with your hands close together in the middle of the keyboard, and it doesn't ever veer too far away from that position. This is what gives it that atmospheric, background sound that characterizes a lot of Glass' music. (Plus he seems to like long strings of alternating thirds in the melody.)

4. The chords used are fairly humdrum chords, and they do not follow the "common practice harmony" tonic/dominant tension/release pattern. The one chord in measure 3 happens to have a little tension, what with the d-flat in the bass creating a tritone with the g. But common practice harmony strongly implies a particular chord for the resolution, and Glass does not follow that pattern. From the standpoint of "common practice harmony," Glass actually leaves the tension hanging for that chord. So if you're hearing a tension-resolution pattern at the beginning of this excerpt, the thing that can decidedly not explain it is the common practice tension/release theory because this excerpt literally does the opposite.

5. In measure 4, there's an a-flat in the right hand creating a momentary embellishment that moves down to g in the second half of the measure. That kind of embellishment was known as a sighing motive in music from the Baroque period, and Chopin often utilized the right-hand alternation pattern on sighing motives that Glass does here.

To sum up: the music circles around itself in a predictable manner, always returning to the same place with pleasing, predictable chords in the mid-register of the piano. So almost regardless of which chords happen in measure 3 and 4, you're likely to hear a) a beginning with the "main" chord, b) a change when you hear different chords (plus that little sighing motive), and c) an answer that begins a new question when the cycle repeats. The cycles are relatively short, and the more cycles you hear, the more deeply you become aware of the pattern.

In conclusion-- the Youtube poster is literally wrong in their analysis of the chords, and wrong about the general category of tension/resolution in the excerpt. But the tonic-predominant-dominant tension/release pattern they suggest sounds similar enough to a "begin-change-repeat" pattern. Since you had a general feeling upon hearing the latter, and since the former suggests roughly a similar feeling, you took it to be objective.

Here's a counterexample with similar two-against-three rhythms:

https://youtu.be/0eEipRR9ebI?t=942

This excerpt uses a deeper range of the piano with a more sprawling voicing between the hands. Each phrase repeats, like the Glass excerpt. But each phrase is longer, and the chord progressions (and hidden melodies in each chord) do use the tonic/pre-dominant/dominant harmonic system that the poster alluded to. For one thing, the phrases don't always return to the same chord at the beginning. Moreover, each phrase pushes forward to the next to create a through-line, one that you can concentrate and listen to all the way through the excerpt to the end of the piece. It's a bit more nuanced that what I can write here, but there is a surprising amount of musical "stuff" happening in these passages that follow a loose set of guidelines for building tension within a phrase and across multiple phrases. The point is this-- if you wanted to make a parody video that put words to this Brahms Ballade, it would begin the same way as OPs video. But somehow, by the end, you'd have gotten a summary examination of Nietzsche's mature works. People from the 19th century thought about music making big, profound statements like that. And the music of that period utilizes an inventive and sophsticated harmonic language that invites that kind of interpretation. The difference between that and the uneventful, cyclic conversation by the guys in the video is for me is what makes the parody video funny.

Finally, lest I be misinterpreted-- Glass wrote his piece long after Brahms, and-- most importantly-- after a long movement of atonal composers took over the role of "serious" music in the U.S. and Europe. I think he was purposely turning the excitement level down to "chill mode" to show that the basic tenets of old school harmony still "resonate" (heh) and by no means were somehow "exhausted" at the end of the 19th century as a lot of pretentious composers claimed during that time. (Although perhaps those composers were just stressed out about the impeding world war and projecting, which is certainly understandable.)

Edit: make my comment even longer with some clarifications.

Edit 2: even longer with even more clarifications

Edit 3: add insult, rank speculation, and finally empathy about pre-war composers

Edit 4: remove footnote digression to get back to a sane comment length

Edit 5: because why not a few more clarifications