Question:

Why is the Latest_Meeting_Start_Datetime_vod__c field blank on Remote_Meeting_vod__c records?

Answer:

The value of the field is getting stamped on the record created in Veeva CRM, and not by the Engage process.

In order to have the value in the field grant the end-user Edit FLS to it.

Related Documentation:

CRM Help Documentation: Hosting a Virtual Event using Engage