Yes, with RingCentral Meetings APIs, you can integrate the scheduling feature, get the joinUrl and meeting id to make a click to join link from your web page etc. Check the API reference and let me know if you have further questions.

Please advise how I would do this.

@Michael Holleman @Phong Vu has already shared meeting API reference : https://developers.ringcentral.com/api-reference/meetings

You can check the meeting schedule APIs. You will get meeting list with uri and meeting id in API response.

I'd like to know how to do this too.

Has anyone successfully built an integration of RingCentral Video meeting to Calendly that works the same as the Zoom or GotoMeeting Integration?  Essentially, I would like to create a new meeting type in Calendly (Video Meeting) and have it automatically schedule the video meeting in RingCentral with a unique meeting link created each time. 

exactly this, in the same way we can select phone/teams would be great to be able to select video meet-other

I don’t know any direct integration. But you can check out the integration via Zapier and Pipedream

https://zapier.com/apps/ringcentral/integrations/calendly

https://pipedream.com/apps/ringcentral/integrations/calendly-v2