From README.md:
If you get a permission denied error, maybe you need to give yourself access to the install folder via sudo chown -R $(whoami) /usr/local/bin.
I really don't think it's a good idea to encourage users to change ownership of system directories. Instead, I propose either installing kitty in /usr/local/bin using sudo, or install it in ~/.local/bin instead. I think the latter is the better option, assuming only a single user needs to have it installed.