onigoroshi: Dame refers to areas that are neither person's territory. If dame were to be marked correctly (which maybe it should be here), then all of the upper portion of the board would be in dame.
If you look at your dame link:
White's upper-left territory is bounded by the stones D9-D8-C7-D6-E6-D5-C4-C3-B2-A2.
White's lower-right territory is bounded by the stones H1-H2-H3-G4-G5-H5-I5-J5.
Black's lower territory is bounded by the stones B1-C2-D3-E4-F4-G3-G2-G1.
Black's upper territory is bounded by the stones E9-E8-D7-E7-F7-G6-H6-I6.
The circled points are neither white's nor black's territory and considered dame.
The point marked 'a' is a potential capture by white if white plays A1 first, so black must fill this in if white plays A1, or take the A1 before white does.

jurek, onigoroshi: The large territory would almost certainly go to white, and should be counted as white's territory. There are places along the border that should probably be reinforced, but they are all miai (http://senseis.xmp.net/?Miai) and would only make a difference of a couple points.

However, my guess why it's counted is that BrainKing's logic doesn't try to guess ANY dead groups, and so the black stones in white's large territory prevent it from marking that as territory. Also, since the game was resigned, there's no need to count them; if you both had passed, however, and marked those black stones as dead, I assume BK would then correctly count the upper territory as being white's.

All white's stones will live; only black's large group will live. Since there's practically no chance of an invasion of white's large territory being successful, it should be scored for white. If, for example, the white group at J8 only had one liberty left with black to move, things would be drastically different.

At any rate, there's no question it would be white's territory. It is not dame, because it is territory: "In the endgame, empty points on the board which are not part of either player's territory and have no prospects of becoming territory." The points inbetween white's border and black's living group are dame, however.

headius: correction to this; I have finished a couple games now, and BK does try to mark dead stones. I would guess that the game in question wasn't counted up simply because it ended in a resignation.