@Barrie Anderson, Thanks for posting in Q&A.
For exe file, the way to deploy via Intune is via Win32. For Win32, the install commands need to support silent install. From your description, it seems the application does not support. So I think it can't be deployed via Intune Win32.
For your situation, maybe you can contact the app developer to see if the app can be installed via PowerShell script or others.
Hope it can help.
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