Luis! You've saved me! We have had this exact same issue - we have a desktop application with a connection string that uses "Active Directory Integrated" as the authentication mechanism, which worked fine on a couple of our development machines, but suddenly stopped working on other machines as we were phasing users over to Azure AD.
I followed the steps you did and found the older version of adalsql.dll was being used on the machines where it was failing, but a newer version of adal.dll was being used on the development machines that weren't having any issues.
We were using this link to deploy (via GP) adalsql.msi to our user's machines, but this appears to be older (non-working) version: https://www.microsoft.com/en-us/download/details.aspx?id=48742
Annoyingly I can't find a more recent version that we could deploy via GP that isn't bundled in SSMS or some other development tool. Do you know of anywhere something like that can be obtained?