You have 2 options to enable this video calling right from Shopify store. One way is via Facebook messenger by integrating the SDK inside. You can have auto-reply to let them call you on Zoom or Skype.
Another option is to have using Intercom along with Aircall for the customer to directly call you from the website - https://www.intercom.com/app-store/?app_package_code=aircall-now&category=phone-and-video
We created the Instaconnect app to add 1-1 live video chat and guided webinars to Shopify. Webinar content is automatically generated from product descriptions and photos, or you can upload your own content.
You can try it for free here:
Hope it helps - let me know if you have any questions and if it works out for you?