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Please excuse the caption 
Ok, so  ,  and  are not particularly worth commenting on other than to say I always like because it sets up an approach in the top right corner quite nicely, when Black plays a 3-4 at R16.
So, 
I tend to approach here in this position too, rather than take the empty corner, simply because I like disruptive fusekis, and taking away the shimari whilst developing in the direction my D16 stone wants to develop I consider to be fun, interesting, and reasonable. It is common for professionals to approach 3-4, 3-5, and 4-5 stones with an empty corner remaining.
Interestingly, one of the problems I find with approaching high, is gote (in tag):
This now allows Black to take the empty corner. Sure, White's top side development is nice, but giving Black this much overall speed and spread in the opening is difficult for White I think. As a result, I try to adopt the following:
This way, trading those two stones for fast development, makes me feel Black has ended up slightly overconcentrated. Actually, I think  is a bit slow, as White can treat the cut as gote and still return to it later at "a" for what feels like an acceptable result. I haven't tried the low approach, maybe I should?
Next move, 
I suppose, based on my last reasoning, this move actually makes a lot of sense to me. Now if White jumps out not only does he want sente, but he risks giving Black profit as well. My instant response would be a temptation to double approach, so as to treat the original stone lightly. However, I'm not sure that works with the pincer, and White's only reasonable move locally may be to jump out. As a result, I suppose I like White's plan in the game more than anything I would have come up with, leaving a huge amount of aji in the top right corner whilst preventing Black from developing the right side.
Should Black have adopted a different pincer? Is this an even result? Should Black have simply extended along the right, making miai of a severe pincer in the top right, and taking the empty corner?
Next move, 
As with my analysis on move 5, this successfully wedges the Black position on the right, guaranteeing easy life because of the ability to make a two space jump on either side, and allowing White increased options should he be allowed to jump out in the top right corner. I really like the precise placement, it feels just right to me.
EDIT: Actually, the other thing I feel about this move is it also feels patient. If I was to tenuki here I'd want to approach or do something I felt my opponent couldn't ignore at all. This feels like the play of someone who is confident in the precise value of what he's doing.
Next move, 
Somewhat surprised by this one. Surely this just encourages White to increase the potential problems in the top right? Ok, Black gets some development in the corner which is never to be underestimated, but it feels like this exchange forces Black to take gote anyway as the top right becomes urgent. I'd take the empty corner myself. However, this also smells like professionals who know how and when to resolve local situations before they become a burden. I suspect Black feels that the top right is already urgent, so it is quite ok to settle the lower right in this fashion and restrict White's options on the right, as Black's next move in the top right corner is forced anyway, and not greatly affected by White's two space extension. I'm speculating, this is above my pay grade.
Next move, 
Feels like the only move. Not doing this is an admission that was an overplay I think.
My expected continuation
At the final position, black doesn't want to take the empty corner because of the risk that White will jump out in the top right, sealing in Black to the corner or launching an attack. My gut feeling is that Black would continue with a contact play in the top right, allowing White the empty corner:
My assessment of the game and players:
Stronger than me. Wouldn't be surprised if they were professional. Every stone feels like it has purpose, and some of the ideas (that, ok, I might be projecting a bit) seem more clever than I would have come up with.
My idea for this exercise would be for others to do something similar, or query / content my points and musings, and start a discussion on possible alternatives and why they feel better or worse than the game in question, or my counter proposals.
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)
) are by far the most common, and black doesn't mind switching it up.