Could it be possible to have league as a batch file, say on a computer where .exe files are disabled? op.gg has replays in batch files so I really want to find a way to get the game to launch from a batch file or even maybe have the code of the exe in a batch or something like that?
Nope.
op.gg does not save replays in batch files. It launches the normal League client executable with additional parameters to download and view a replay (which it has stored on its own servers). op.gg and other sites are just saving a link in the batch file.
A batch file can only execute commands that you could execute yourself on the command line. And if executables are disabled, then you won't be able to circumvent that just by writing a batch file.
Your description of the situation seems odd, though. The vast majority of what happens on your Windows PC is a .exe. If you could find a more precise description of your problem, then there might be a different way around it. But everything from the Windows shell (showing you your desktop and icons) to your internet browser to Task Manager is running as an .exe.
