I finally found a way to do this based on a few tutorials like this one. I had to create a new provisioning profile to deploy to other Macs and for this provisionning profile I had to add each Mac machine on which I want to test my app with the "Add a device" on Certificates, Identifiers & Profiles.
Then I had to refresh the list of signing identities in XCode
in Preferences
=> Account
and had access to the new provisioning profile. Then I Archive
, Distribute
my build and export as an Application
that I sign with the given provisioning profile and then the App properly launches with sandbox for the AppStore on other Mac computers.