So my question is if it is possible to install such updates without the actual need of restarting the game.
No, wyUpdate makes the assumption that all files of your app are dependent on one another (thus all exes of your app need to be shut down). Your best option is to install the updates immediately on the next start of your application (the default behavior of the AutomaticUpdater).
Of course we may run the update process at the very beginning when no window is actually shown and the user wouldn't even notice the game was restarted but we want to show to user there are new update available and we do so by displaying our custom graphics rendered on top of the main menu using our rendering pipeline.
Using the AutomaticUpdaterBackend you can implement the custom updating UI for the checking, download, and patching steps. However, to install the update you'll still need to restart your app (or leave it until the next start of your app).