I get the same problem with valid solutions that don't match whatever it's comparing as the "right" one. It would be better to instead do a goal test after the final square has been filled? Seems to me this wouldn't be too hard to implement instead of comparing with a key.

Nope, there's just one: look at column 1 and 4, so far they are the same.

That's the point.

The rules don't explicitly say that columns need to be unique (only rows).

Within the stated rules there are (as best I can see) 2 valid solutions to that puzzle. It is the introduction of the unstated unique column rule that resolves it.

The author is not a native English speaker, but it seems obvious that the row rule should apply to columns.