What API / admin permissions are needed to use Gmail Gopher? Why?

Because it offers such tremendous power,  Gmail Gopher is restricted to use by G Suite domain super-administrators only.   

The G Suite domain must have API Access enabled, and the the spreadsheet tool must be separately installed by each end-user an Add-on for Sheets available in the Chrome Web Store.

The API scopes requested by the Sheets Add-on are as follows:

Scope

Reason
View and manage your spreadsheets in Google Drive. Used to spawn, format, and import data within the current Sheet the user is running Gmail Gopher within.  No spreadsheet other than the currently active Sheet is ever accessed.
Display and run third-party web content in prompts and sidebars inside Google applications. Used to render the custom sidebar and modal dialogs within Sheets.
Connect to an external service. Used to make calls to Google Analytics (with anonymous reporting info) and Google Cloud hosted infrastructure and as well as a database that backs the tool.  Data retained in Amplified IT's custody includes the email identity of users who performed actions within the tool, as well as aggregate information about their actions.
View users on your domain Used to confirm that the currently logged in user is a super-administrator, a requirement for use.

Gmail Gopher also requires one-time installation as a G Suite Marketplace App, which requires domain-wide access to the following API scopes.

Scope

Reason
Read, send, delete, and manage your email. Gmail Gopher needs full access to user inboxes to perform its mass message search / delete functions.
View your installed application's licensing information. Used to ensure the correct installation state of the app.
View and manage your spreadsheets in Google Drive. Used to write status messages and logs back to Google Sheets when performing bulk operations.
View your email address. Used to identify the currently logged in user.
View your basic profile info. Used to identify the currently logged in user.