After installing Mafia Trilogy, When I ran Mafia 1 and Mafia 3, Bitdefender detected mafiadefinitiveedition.exe and mafia3definitiveedition.exe as infected application and remove it.

False positive ?

For mafia 2, the launcher is not present but the shorcut is present in the folder.
Missing file in the installation package ?

Thanks,

As for links. Did you use GOG or GOG Galaxy versions?
That happen for me twice for some older games older installers 2.x.x.x generation. Links are created in game folder, but empty. While Desktop ones are correct. Just reinstall it. To folder like X:\Games\Mafia-1-DE\.

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Force BD to update and it Database update. Turn off. Reinstall. Force recheck game folders. if same happened - most likely false detect. You can use VirusTotal as well. But VT not 100% acurate. Microsoft and MalwareBytes do report as some detected there (force re-scan on website if it outdated), but current checked for updates apps on PC not detect anything. Happened at least twice for me.

VT have additional information. For what else files and net resources exe file refered. Even if it DRM-free, if there is connection it actually can try to connect some 2K statistic servers. Its not aa big differences from GOG Galaxy builds which ones have achievments (and galaxy related dll that send statistic to net).
So some leftovers from online interactions in exe\dll files can be detected by security software as malicious. Maybe there is white-list in your security applciation Db for Steam and GOG Galaxty clients, but deffinetly not for separate games. better add X:\Games\ folder to exclusion.

Kepp in mind that 3rd party apps also do strong restrict system Program Files folder. And if use admin_rus is partially enough for Microsoft Defender (at least for main exe file it added to exclusion, but since this is system folder - not whole game folder), 3rd party apps still protect this folder.
Do not install game-related clients and games to Program Files.

*Normally game should work in compeltely offline mode, and not try to listen any response from any online servers. But some DRM\online leftovers really can be left in exe file and prevent game from normally working without online connection. There is at least one example of it on GOG (They Are Billions).
But it is not related to security apps. Security apps higly possible detect something even for normal realisation of exe file where online interactions is optional.

Installed from the off-line installer. BD is up to date.

I have 48 GOG games installed and I never seen this problem before.

No problem with the Mafia III normal edition.

I restored exe files from the quarantine, scan with BD and not problem found. I restart the 2 games without issue.

May be BD found something at the first run of Mafia 1 and Mafia 3 with the launcher.
This problem not happend whith Mafia 2 but Mafia 2 doesn't have a launcher.

If you find files that are definitly harmless but blocked by BD, report them as "false positives". This way they can implement an exception in the standard version for all users.