Do you mean a little cloud symbol? IF so, and if it's in the App Store, it's telling you that you had downloaded the app at one point, but it's NOT installed on your Mac and is offering to download it again. So, basically, you have NOT installed Outlook. It won't appear in your AppleID iCloud account online because iCloud doesn't have anything to do with it.
So, you need to actually install Outlook on your Mac if you want to run it.
Installing MS products is not like installing other things on your Mac.
One place to look for Outloon is in the Launchpad. Apps from the App Store usually show up there. On my system, Outlook is also in the Applications folder under my account login name. Click on FInder, look in the left sidebar for Applications, go there and look for "Microsoft Outlook" in the folder. If it's installed, it will be there.