I can confirm that what Van is saying is correct.

The input methods do /work/ correctly, so just the docs are wrong.  And
that particular chart is hardcoded (i.e. not generated).  I did a bit of
git spelunking and it seems to have been wrong from the start; probably
just an accidental omission.

Without diving into a full explanation of how these input methods work,
if you select any one of these input methods and type any of the QWERTY
keys in the chart (and press SPACE to finalize the selection), you'll
see the corresponding Chinese character appear in the buffer.  K does,
in fact, produce 大, as a person familiar with Cangjie would expect.
Wikipedia has a decent page[1] if you want to learn more.

I hope that's helpful.  Patch attached.

[1]: https://en.wikipedia.org/wiki/Cangjie_input_method

-- 
Cameron Desautels <camdez@gmail.com>