There are two possibilities I can think of. Either the files were created with some weird combination of permissions and ownership on the filesystem, or there’s another process that keeps an exclusive lock on that file.

Are there multiple Windows users on your PC? Did you check the permissions for the .exe file? From what I know about BattlEye, it’s basically a kind of a rootkit, but I’m not sure if it circumvents normal permissions to the file or not.