Recently this error started popping up for some Gmail accounts:

[Google Contacts] Synchronizing folder 'Your Google Account/Other Contacts' failed due to the following error: Parameter validation failed for "resourceName" : The value did not match the regular expression ^people/[^/]+$

This error means there has been a problem getting some contacts synchronized from the Google server, specifically in the 'Other Contacts' folder.
This folder works similarly to eM Client's Recipients history - it's Google's folder for saving email addresses you previously sent messages to, so these are usually not contacts created by you, but automatically by the server. Your contacts are in the main Contacts or My Contacts folder. 

Deleting the contacts from 'Other Contacts' and then repairing the folder in eM Client should resolve the issue.

Other Contacts cannot be deleted from external apps though, so you need to go to this page in your browser: https://contacts.google.com/other
Make sure you are logged in into the correct Google account and then delete the items in this folder.
Back in eM Client, open the Contacts section.
Right-click the Other Contacts folder and open Properties
Open the Repair tab and click Repair.

This will re-synchronize the folder and without the invalid contact, the error should not pop up again.