The new 'old' games that are now on the BDA

I bought Diablo 1 from GoG a while back and it is currently installed.

However, the BDA doesn’t see it and thus is telling me I have to buy it.
(Even despite copying the “Diablo” folder to the “Program Files (x86)” folder.)

We don’t have to buy it again in order to play it through the BDA, do we?

EDIT: I’ve recently learned that other copies of the old games will not work through the launcher. They all need to be purchased through Battlenet for them to work through the launcher.