Yes the client gets Admin access otherwise they can’t see the forms, add events, etc.
I just logged in as an author and got this message:
Sorry, but you do not have the correct permissions to install the Cardinal Demo Content and Contact Form 7 plugins. Contact the administrator of this site for help on getting the plugins installed.
Sorry, but you do not have the correct permissions to activate the Go Pricing Tables plugin. Contact the administrator of this site for help on getting the plugin activated.
Also, I can see the Events, but am unable to see the Gravity Forms, WooCommerce or Job Listings.