To share outside the organisation, the user requires an account to provide a method of authentication to access the resource. Without this, the folder or file would be effectively public (this is true of all cloud based file storage systems, such as Dropbox, etc.). The user can create a Google Account with any email address (the domain may need to be whitelisted by the IT team, reach out to [email protected] if unsure).
Once the email has been added to the shared resource, if they don't have a Google Account, they can create one here (this is also in the email they receive when the file/folder is shared with them). To use their own email address, as apposed to a gmail.com email address, they simply need to select the "Use my current email address instead option" on the form...
When clicked, they will be able to enter their full email address and create a Google Account with that in just a few simple steps...