Okay, thanks for the screenshot and your prompt reply.
Yes my guess was in the right direction, as I think the executable file has been renamed to Bioshock2HD.exe, from Bioshock2.exe, IMO.
Though I’m not 100% sure, but for the first title which is, BioShock Remastered, the exe file name has been changed via the latest patch/update.
Give this a TRY. But first, make a BACKUP of the file you are trying to edit (“very very Important”).
Try to rename Bioshock2HD.exe, to Bioshock2.exe, and check whether doing this, allows INFINITY to detect the Game or not ?
Remove HD from the file name.