After that example the book goes on to explain the previous examples:
So maybe we can try understand the values there, and then maybe even martin’s examples, given the previous two posts.
I did the same kinds of marking for the chilled game, this time 11 points each.
a) was the same as (c) from the last game so it’s *.
b) is the same as (a) of the previous game so it’s ↓
So then the value of the position in the chilled game is ↓* or ↓+*, and so if White moves to take * then they can win.
Again I’m 100% sure on how the score intereacts with the infinitesimals and rounding. I might have to get further into the book to get a better feeling for that one. I can guess maybe that the score is 0+↓ after white’s move, and then that rounds to -1? or white winning by 1.
Again in this game I marked the territory for the chilled game. The two values A and B are the same as the previous game but C maybe needs to be calculated.
c) If black moves, they gain a point but also a marking so that’s 0. If white moves, they gain a prisoner which I guess is cancelled out by the marking they have to add, and then I guess there’s just two dame left, one for white (connect the ko shape), one for black to connect the groups. I guess maybe the connection for white is sente, but yeah maybe the value is just {0|0}=*. The book does seem to suggest that it is * so this would be my understanding of that value.
So then the whole board in the chilled game sums to * + * + ↓ = ↓, because * is it’s own negative. So if white plays they can “round” ↓ to their favour. So when white plays (b) they move both the local position (↓) and the global position to a value of 0, and that should be the winning move.
That said again, I need to read more to understand how the chilled game values get rounded to affect the result of the normal game by one point, but still maybe understanding these figures is a good start.
I think in order to attempt @martin3141’s examples, one probably needs the section 2.5 on tinies and minies, because there’s large numbers of stones to be captured or saved.
I start to run into things like {3|-3}=±3 for the area in the top at F1, and the bottom I’m evaluating as the mess {4|{0|-2}} in one of the positions. The first value seems to have mean 0, but the second one doesn’t, so maybe one needs to mark it differently and learn properly the ideas involved in chilling and marking.
But to be fair, I still need to learn how to count those positions properly without infinitesmals 
Section 2.6 just seems to be fairly hard to read in isolation and it does say “the reader should not feel obliged to understand the method yet”.
So maybe that’s a good point to just give up on Chapter 2 for the moment, put a pin in Martins positions, at least with respect to the infinitesimals, and then read Ch 3 about chilling?