desk doesn't seem to execute desk file at all about desk HOT 1 CLOSED

Not sure if you had figured this out yet or not, but I had the exact same issue.
In my case, I used homebrew to install, and according to the docs, if you brew install desk, it automatically sets itself up. However, I already had a pre-existing .desk/desks folder, so I did a "brew install desk" and then copied my .desk dir into place. The issue you list above is exactly to what I experienced. It turns out, the directions are incorrect.

I had to rm -rf ~.desk, and then "desk init" and then copy my .desk directory back into place.
turns out, desk init adds the following to the .zshrc:

# Hook for desk activation
[ -n "$DESK_ENV" ] && source "$DESK_ENV" || true

Hope that helps. The documentation should be updated, or the brew install should be fixed to modify the .zshrc

from desk.