Howdy AKs0n,
It looks like Overwatch was purchased on the Battle.net email that you used to log into the forums, so you don’t need purchase it again.
When a game is purchased on the Battle.net online shop, then it is linked to the Battle.net email, which means you just need to log into the Blizzard app with that email to install the game on any computer. If you see an error that the Overwatch license is missing, this is likely a bug that is described here.
If you have any other questions about account purchases though, then it would be best to create a support ticket to discuss those questions.