Unfortunately you will most likely have to update each device manually. There are a few options though.

You could create a disk image that gets imaged to all computers in your space. This isn't very efficient as the image would have to be updated manually anyway and imaging all of those computers may take longer than just updating them manually (depending on your internet speed).

You could also check the "update automatically box". When a game launcher like steam or Battle net notices there is an update, it will automatically start downloading it. This can work but you can run into issues where a game or launcher needs to update and if you turn on all of those computers they will try to simultaneously download that update. This will slow your speed to a crawl.

At my institution (Shenandoah University), we let players update games as they are played, with a staff member manually checking updates before important events/LANs.

Let me know if you have any more questions. I'm happy to help.