The M8 point is territory.
The most important thing that we have to have in mind is that the life and death status of each group is analysed independently of all the others, under Japanese rules. So, first of all we determine the life and death status of each group, performing one analysis per group (most of the time things are obvious of course and we don’t really “analyse”).
A group of player 1 is dead under Japanese rules when player 2 playing first could achieve the following goals in a hypothetical game continuation without any chance of using ko threats other than simply passing (ko threat situation is irrelevant in this particular game, but this rule explains why bent four in the corner is always dead, as well as moonshine life, etc):
- Capture the group
- Prevent player 1 from placing a new permanent stone in the locality of the group
“Permanent” means that it can never be captured. “The locality” of the group is tricky to define, but intuitive: in this game for example, when analysing the life of the black T9 stones, black being able to place a new permanent stone in S14 is irrelevant and not in the locality, but if black would somehow be able to place a new permanent stone at T7 or even K4, that would count as new permanent stones in the locality of the group. Section 7.1 of http://home.snafu.de/jasiek/j1989c.html explains the locality idea formally, but an intuitive grasp is more than enough for almost every purpose. Another example of this locality idea appears in http://senseis.xmp.net/?SekiInAreaAndTerritoryScoring: Once the seki is stablished, the two corner black stones can be captured inconditionally if white plays first, but doing so enables black to play two new stones in the locality, and so the black stones are considered alive as is.
So, with that main important points cleared up, we can go back to this board. First of all remember, each group has to be analysed on its own, so we will do so for the relevant groups here:
- L5 white stones: Black playing first can never force a capture on this group. White is alive.
- N9 white stones: Again, uncapturable, so white is alive.
- S10 white stones: Trickier but also uncapturable: if black tries to capture, he has to fill T10 and is captured first and there is nothing left to do.
- T11 white stones: Same as S10.
- T8 black stones: This stones can easily be captured: white would just fill M8 then T7 then capture. If black tries to resist playing T7 or T10, he puts himself in atari and is captured. Furthermore, once black is captured it is clearly impossible for black to place any new permanent stone in this area: white position is strong and rock solid. So these black stones are dead.
Notice that the analysis is always done independently group by group, and the analysis is not actually played, it is just hypothetical. Here, the analysis gives a status of “the black stones are dead, the white stones are alive”. So, black stones are removed as prisoners because they are inside white’s territory, and M8 is counted as territory.
Note that white group is not in seki: A group in seki is defined in Japanese rules as an alive group being in direct contact with a dame (this presumes dame filling has taken place). Here, the white group touches no dame, only its own points of territory since we already know that the T9 black group is dead. So there is no seki. If O9 somehow and for some reason had to remain unfilled, for example, that would be an example of dame, and that would be seki for both groups touching that dame. This is very important because a group that is alive in seki has no territory, and enemy dead stones would not be removed as prisoners from inside a seki but left on the board.