OK, I've listened, and have a few extra observations...
Firstly, chord names:
The G7 in the intro and verse is G7/B (no big deal, just tells you B is the bass note);
The "F9" (more important) is actually Fmaj9. (F9 is a quite different-sounding chord.) It's not a complete Fmaj9, as there is no A, and you could look at it as a C triad on top of an F power chord. "Cadd4/F" sums it up pretty well, and may be a better name (for that reason) than Fmaj9. Take your pick.
For what it's worth, I hear the key centre here as D minor, but with a definite dorian feel (thanks to the G7/B). The repeated Fmaj9/Am pair of chords at the end don't nail Am as key chord for me, but this kind of thing can be subjective. The pitch collection is certainly all from C major, so we have some kind of relative mode of C major; whether you want to call it A aeolian or D dorian (or C major/ionian!) depends on how you hear it.
There is a hint in the vocal that the key is C major, as it seems to resolve there after the first 2 chords - and Dm-G7 (in other circumstances) would definitely indicate an approaching C major centre. But of course the chords under the vocal there are Fmaj9 (or Cadd4/F) and Am, which prevents the resolution. Technically, you can call this a "deceptive cadence" in C major. (Dm-G7 goes to F instead of the expected C.) But my money - given that this is rock and not classical music

- is on D minor, in the broadest sense. Whenever they hit that Dm, it sounds like they're thinking of that as their base chord, their central focus. Then they're just following that with chords they think sound good.
In what that tab calls the "pre-chorus" , I hear those chords as straight Bb-Am-G (triads), without the C and E on top of the Bb. (And the bass on the G this time is G, not B. In the bass I mean, not necessarily on the guitar.)
(I wouldn't call this a "prechorus", as it isn't followed immediately by the chorus. Not sure what I would call it, mind you. It's not big enough to be a chorus itself, and is more like a short bridge section.)
This is an odd set of chords keywise. Bb and G don't belong to the same key (are harmonised from different scales). But they still work in a "D minor" context because Bb comes from D aeolian (natural minor) and G from D dorian. (Mind you, you can also "explain" Bb as a bVII in C major, which would be a very common usage in rock. But I suspect they're still thinking D minor/dorian as their home tonality. They're refusing to go to C anywhere, at least, as Malcolm points out.

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The "pre-vamp" is simply the intro repeated. "Vamp" is a better term than "pre-verse" (nothing wrong with the latter in principle - describes it very well - it's just not a conventional term). It's the same sequence as the verse anyway,
music lessons for kids.
The "chorus" is not a chorus, however - purely because there is no vocal on it! ("Chorus" by definition implies singing - unless, arguably, the whole track was instrumental.) This riff section is an instrumental "bridge" - and the implied key centre is clearly D, and mostly minor pent apart from that odd passing F#.