The main sections missing are some half lotus postures while in desk pose at 01:17 which leads into Uttana padasana and Urdhava Danurasana (wheel), I guess as counter poses. At 01:48 there should be a Supine leg behind head subroutine with a couple of prep poses that leads on into Yoga Nidrasana (sleeping yogi). At the end of the sequence at 4:29 there should be Savangasana Mandala (circular ambulation), this is very silly but I quite like it. I used to try it last summer and have a video from my phone which gives the general idea. Sadly, now I'm upstairs, I don't have the room for it.
So I'm calling this a simplified version, if it wasn't speeded up it would run to about twenty minutes and misses out the tricky LBH asanas. Normally in Supine I would go about the Leg to chest, Arm/leg raises and Desk poses much more slowly, longer stays etc. but this, as I said, was originally filmed as part of the Inverted sequence and I tend to use these poses there as prep postures.
As I've mentioned elsewhere (link to come), there would be some Sury's and some standing poses before this sequence and some finishing poses afterwards, similar to Ashtanga but taken from some of the other Vinyasa Krama sequences depending on what seems most appropriate.
NB. Ramaswami recommends practicing the sequences in this way to gain familiarity with the asanas and, I guess, their groupings. Once you have a better idea of the range of asanas your better able to develop an appropriate practice. I'm looking forward to finding out more about this in the summer. I know he has a handful of key asanas that he recommends practicing every day. I assumed that you would practice those and then fit the other asanas around this framework in a similar way to how the Ashtanga series are formed. However, in one of his other books he seems to suggest that Krishnamacharya would have him practice the same kind of asanas within a lesson. I'm guessing one day the key asanas plus some Bow sequence subroutines another day the keys asanas and some inverted subroutines. The point being, these aren't fixed-in-stone sequences, adaption is the name of the game.