We don’t want to check the “lync.exe” regapp since we don’t want the relevance to target only Lync/Skype for Business.
I would expect the fixlets for KB4475519 to become relevant for systems with Project 2013 SP1 installed since Project 2013 contains a component targeted by the update.
Updates for the Office family aren’t restricted to the specific product labeled by the update. If the update patches a shared office component, then the update will apply to any Office product (whether Word, Project, Excel, Skype for Business, etc) with that shared component.
This is easily demonstrable by installing a standalone Office product like Project or Skype for Business and doing a Windows update scan. The scan will return updates labeled for Office, Word, Excel, etc… all of which can be applied despite not having those specific products.
This is basically explained in Scenario 3 from this KB article: https://support.microsoft.com/en-us/help/830335
The team did some testing on your specific scenario and were able to apply the KB4475519 update on a system with only Project 2013 SP1 installed and on a system with both Office 365 (2016 version) and Project 2013 SP1 installed.
Is your Project 2013 at the SP1 level?
Another thing is maybe try a repair of Project 2013 and/or Service Pack 1 and try reapplying the update.