Android - Can't install previously installed apps from Google Play

The issue here is that the uninstall process wasn't registered at Google Play Store.

Without the uninstall process registered, Google Play Store still reports the app as installed on the device that's associated with your Google account.

To overcome this, you need to manually trigger the uninstall from the Google Play Store, within the "MY ANDROID APPS" list:

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Step by Step

I have a couple of apps that I've uninstalled from my device and the uninstall process wasn't registered at Google Play Store. I'll use one as a guide:

1. Access "MY ANDROID APPS" list, search for the desired app and click the recycle bin icon to trigger the uninstall:

   

2. After confirming, the app will get marked as "removed":

   

3. Now you can access the application at Google Play Store, and install it like you mentioned that you prefer to do:

   

Error message still appearing

If you've signed in to your device's Google Play Store app, downloaded an item, and your device doesn't appear on the Google Play website, you can try clearing your app's data by following these steps:

1. Open your device's main Settings menu.
2. Select Apps or Application manager (this may be different depending on your device).
3. Select Google Play Store from your list of apps.
4. Touch Clear data.