When you buy digital media, whether physical or digital, you are buying a license to be able to view it whenever you want. You do not own the media. You don't own the rights to that game just because you have a physical copy of it, you don't have access to the source code, and it is still riddled with DRM. The same applies to movies and music as well.
At the end of the day, whether a piece of media is stored on a Blu-ray/DVD or an HDD/SSD makes little difference. If all ownership means to you is being able to access the media you've purchased a license to consume regardless of its online status, then archive it. Your SSD or HDD is as much a physical media as a Blu-ray disk.
Chill dude, all it means is that it is a) free to claim, and b) you get to keep it as in you don't just get to trial it for a weekend which is commonly seen with "free weekends" on steam.