I am confused as to how seki is scored. I thought it wouldn’t count. But in this game it did count (bottom right corner) The points went to my opponent and he explained in the chat why.
OK…
But then in this game (top middle) it didn’t count. What’s the difference please?
In addition to what _KoBa said, I’ll point out that your opponent in the first game seems to misunderstand sekis. In the comments they seem to think that if it is surrounded by a living group it can’t be a seki and the territory belongs to whoever surrounds the region in question. They also say that if neither player can do anything good then both coloured stones are considered dead. This is all wrong, and your intuition that if it was a seki the stones of both colours would be alive is correct. But, as _KoBa pointed out, it is not a seki.
For the first game, you should look into Farmer’s Hat (T-shape). It is a killable shape and black has a right to kill it at any time, so white group is considered as dead stones.
I put the killing variation for the first game. For the second no one can kill ( if one try, he gets captured and the resulting shape is full of possible eyes) so it’s a Seki.
More than confusing me with the strange explanation, my opponent annoyed me insinuating that I pretend not to understand and that derailed my thinking. I could have just figured it out myself.
In all honesty, your opponent’s explanation was bad and mostly wrong. The true answer is that it isn’t a seki because black reduced your group to a dead shape. He can force you to capture his stones and then immediately block the key point needed for you to live.