At first I thought this was right, too, and would mean only 8 checks, but it is possible to have a diagonal choke point that doesnt follow this. Example:
xxxx
ooxx
xxoo
xxxx
This is a lot more difficult to evaluate, especially considering it could just as easily be:
xxxx
ooxx
oxoo
oooo
At which point, simple qualifications might make the first spot a potential choke point. (This is kind of a problem with the original proposal as well.)
There needs to be something tangible beyond the choke point, for it to have actual value, and that is something the AI may never understand (at least in this game).
Circle gets the square...
In the first grid, the simple check would decide that each of the 'o's was a chokepoint, and that is actually true. A second check might be required to decide whether to build on any one plot, involving borders, also actual plot contents (less likely to build on a resource, more likely to build on a hill, etc).
In the second grid, indeed a "false" chokepoint is indicated. I don't have an immediate answer to this.