I just installed an application (from a developer in which I trust) that hasn't been reviewed by Shopify, and it is used in multiple merchants.
As I'm currently submitting my own application, I was wondering how can that be, since Shopify tells me my only option to have multiple merchants using my app is to go through the review process.
You can see that even with the "Not reviwed" message, it still says I can install the unlisted app. What am I missing?
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What you're missing is the fact that you yourself (through your own development store) are installing your unlisted, unapproved public app. If you attempt to provide the OAuth installation link to another merchant, they will get an error that they are unable to install your app (I found this out the hard way).
I don't know why you were able to uninstall a non-reviewed public app, I think older apps might be grandfathered in.