In Inno Setup, one can use CloseApplication to enable the Windows restart manager, and check for running instances. This, however, does not apply to the uninstallation. The setup removes all files that are not in use, and shows a message along the lines of "not all files could be removed, please remove them manually".
The only way to check for running instances that seems to work during uninstall runs, is to use AppMutex.
Is there a way to enable the restart manager during the uninstallation as well?
No, you cannot use restart manager in uninstaller. But you can code it yourself:
How do you close then restart explorer.exe in Inno Setup uninstall using the Restart Manager?
Simpler, but less elegant solution is killing the application in
InitializeUninstall.For that see my answer to Uninstall fails because program is running. How do I make Inno Setup check for running process prior to attempting delete?