Rockstar Game Launcher and Ownership

Will uninstalling a game from Rockstar's new game launcher void my ownership of that game?

I have claimed the free giveaway version of Grand Theft Auto: San Andreas, like many others did, but now I want to uninstall that game. Will I be able to install it again later, linked to the same Social Club account?

No worries, once claimed, it will be tied to your account: it's a free game, not a trial version.

For verification, this image was pulled from the official Rockstar Games article announcing the giveaway as part of the release of their official game launcher - mentioning a "FREE" copy:

The launcher works as any other (Steam, Epic Launcher, Uplay, GOG Galaxy), in that you can install and uninstall games whenever you feel like it.