Hi,
Ruairi from Shopify here :)
You can use an app like Events Calendar to display a list of events, this uses Google Calendar as the calendar management tool: https://apps.shopify.com/events-calendar
You can also embed a Google Calendar directly by following this guide: https://docs.shopify.com/manual/configuration/store-customization/page-specific/welcome-page/can-i-add-a-calendar-with-all-of-my-workshops-to-a-shopify-page
Using the Agenda view displays the calendar as a list of events: https://productforums.google.com/forum/#!topic/calendar/6nEUjaxAEPU
The color, size, and other options can also be set when you are editing the calendar to embed: https://support.google.com/calendar/answer/41207
Using either of these methods would allow your client to edit the events from within a Google Calendar account and the changes would reflect on their Shopify site.
- Ruairi H