What is the executable used for Batch Files in Windows?
It's actually COMMAND.COM or cmd.exe.
When a batch file is run, the shell program (usually COMMAND.COM or cmd.exe) reads the file and executes its commands, normally line-by-line.
It might be helpful to know that specifically not allowing either command.com or cmd.exe wouldn't be a good idea. Windows being unable to launch either COMMAND.COM or cmd.exe would result in undefined behavior.
Batch file
This is because I want to allow a bat-file to the to run when this GPO is enabled. It'll be even better to specify which batch files are allowed to run. It can't be (cmd.exe), because that's in the "Specified" list in the local GPO and batch files are still not allowed to be executed. How do I include file.bat along with other executable to be allowed to run?
If you have allowed cmd.exe to be executed, and the .bat file is still blocked, then you have likely prevented a user's access to the command prompt.
Also, if users have access to the command prompt, Cmd.exe, this setting does not prevent them from starting programs in the command window that they are not permitted to start by using Windows Explorer.
The solution to your problem is using something other than a batch script. If you were to use PowerShell, there is an executable you can allow for that,
Source: Configure and allow Windows to Run Specified Programs only
cmd.exe
...