I don't know that I would think of this as being in a "key" per se. It sounds to me more like the harmony is organized around transposing similar chord structures and shaping the melody around scales that fit those chord structures. I'm curious where you got the midi file for this? There is a spot or two where I question it's accuracy...
If I look at m.2-5, the bass is sitting on G while the Horns and "Baroque Trumpet" (whatever that is lol) are all playing notes that fit into either a G mixolydian or G dorian scale. There is no B or Bb present, so it's ambiguous which it could be here, but I would suppose this ambiguity is the effect the composer was going for.
m.6-7 is where I question the accuracy of the midi file a little bit. At a first glance it appears that the harmony is just shifting between different Maj7 chords in first inversion. Starting on Cmaj7 on the downbeat of m.6, then moving the Dmaj7 on the upbeat of the second beat, Ebmaj7 on the downbeat of m.7, and finally Fmaj7 on the upbeat of the second beat. The only thing that throws this off is the bass plays an F natural instead of F# on upbeat of m.6, while the rest of the ensemble is playing F#'s. If the bass were playing an F#, it would fit the pattern.
M.12-15 is where things get interesting. Looking at just the trumpets and bass, he shifts between different transpositions of minor triads in first inversion, with a couple of major triads in first inversion in m.15. The sequence is Em, Gm, F#m, Amaj, Abmaj, Fm. If I look at m.12-13, every note that is played between the Piccolo, Trumpet and bass in within the G half-whole octatonic scale (G G# A# B C# D E F). In m.14 he then uses the A half-whole octatonic scale (A A# C C# D# E F# G) to match the F#m chord, the only oddball is the F natural in the piccolo. In m.15 he uses the C# whole-half octatonic (C# D# E F# G A Bb Cnatural) and the C whole-half (C D Eb F F# G# A B) over the Amaj and Abmaj respectively, and finally the Ab half-whole over the Fm (Ab A B C D Eb F Gb Ab) M.12-15 is a repeat of m.8-11.
M.16-21 appears to be stepwise movements of Fmaj/G in m.16-17, Gmaj/A in m.18-19, and Amaj/B in m.20-21. Notice the stepwise movement in the bass that leads to the C in m.22.
M.22-25 alternates between two different mixolydian textures, first on C, then on B. The cycle then repeats starting at m.26. I think the mixolydian serves as kind of a cadential point to make it feel like the whole piece is about to resolve back to the start. The mixolydian mode has always had a cadential feel to me, likely since it associated with the V in tonal harmony, so I think it tends to serve the same cadential function here, even though in the end it resolves to a chord on G instead of an F or E you would expect from C7 or B7.
The above is just the way I look at it, and not necessarily the "correct" analysis. My point is that there is a lot of music that doesn't fit into the traditional idea of a "key". When I think of something as being in G major, I expect to find chord progressions like ii V I and V IV I that emphasize G as the tonic, which I don't find here.
Hope this helps. Feel free to point out any errors in my analysis.