This issue is particularly annoying and I only just discovered it today for the first time.
Here’s an example of what it looks like
In order to install the application so that it bypasses Gatekeeper, you can rerun
brew cask install like so:
> brew cask install --no-quarantine blah > brew reinstall --no-quarantine blah
If you’d like to keep this flag enabled all the time, and honestly you might as well, you can also do the following:
> export HOMEBREW_CASK_OPTS="--no-quarantine" > brew cask install blah