sqlrob: I mean the games.
Most of the games (Sword of the Stars: The Pit for exampl) don't actually require admin permission, so it is perfectly fine to turn it off. Some of the games (Jagged Alliance 2) may require admin permissions, depending on where you install them. The v2.x installers do try to avoid system protected folders, but you can still install them there. A few of the games do require them, because the developers tend to not know proper coding practices (HKLM instead of HKCU keys for example). The "Run as Administrator" setting is usually the first troubleshooting step, so GOG has it already set to reduce the support tickets.
If you are aware of why the flag is not needed, feel free to remove it. If you have no clue about it, then you probably don't know why you should set it, so it's best if it's already set.
And a small nitpick, the limited user rights have been standard from 1993, with Windows NT, which did have support for per-user settings. But no, game developers still opted for system wide settings instead...
Edit: ChrisSD tells me that DOSBox proprely reads files stored in the VirtualStore folders, so DOSBox shouldn't care about admin rights.