Glasper is a genius, I love his music. You should hear his version of smells like teen spirit. Good luck on trying to play this at your audition, you're gonna need it, lol!
I've listened to it a few times and have put together the complete arrangement for you, every single bar. For the sake of simplicity, I've counted mostly as though the bass drum you hear would be 1/8 notes, but at certain points it was appropriate to count as 1/4 notes where I've put 4/4 and 2/4. The music informed my ear that it felt right at those sections. Certain crashes and tom fills informed me where a 2/8 bar was appropriate instead of a straight through 10/8 or 4/8 bar. But I've put alternative counting as well in brackets if you prefer those.
I hope this helps. I've also put the video times where the sections change.
0:00 - 4/8, 4/8, 4/8, 4/8. (*Or if you prefer, 4/4 x 2 bars)
0:05 - Keyboard melody starts 4/8, 4/8, 4/8. (*Or 4/4 + 2/4. *Or 6/4)
0:09 - 4/8, 4/8, 4/8, 4/8, 2/8, 2/8, 10/8, 10/8, 4/8, 4/8, 2/8, 2/8, 4/8, 4/8.
0:30 - Vocals 10/8, 10/8, 10/8, 10/8, 10/8, 10/8, 2/8. (*Or 5/4 x five bars + 6/4)
0:50 - Instrumental 3/8, 3/8, 3/8, 3/8.
0:54 - 9/8.
0:57 - 10/8, 10/8, 10/8, 10/8. (*Or 5/4 x 4 bars)
1:11 - Vocals 10/8, 10/8, 10/8, 10/8, 10/8, 10/8, 2/8. (*Or 5/4 x five bars + 6/4)
1:31 - Instrumental 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8.
1:40 - 4/4, 2/4.
1:44 - Drums drop out and it's 8 bars of 4/4 building into....
2:05 - Long instrumental section, 12 bars of 10/8. (*Or 5/4 x 12 bars)
2:46 - Vocals 4/8, 4/8, 2/8, 4/8, 4/8, 4/8.
2:53 - Instrumental 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8, 3/8.
3:09 - Tacet for 2 bars of 4/4.
At 3:15 - Vocals [[: 4/8, 4/8, 4/8, 4/8, 4/8, 4/8, 2/8 :]] Repeat this sequence till fade.
You could also count this section as 4/4, 4/4, 5/4 instead.(effectively it's like 13/4)