When I was in primary school, the librarian used a computer this way, and it worked fine. However, she had to back it up daily or weekly onto a stack of floppy disks, and if she wanted to serve the students from the other computer on the other side of the room, she had to restore the backup on there, and remember which computer had the latest data, and only use that one. When doing a stock–take (scanning every book on the shelves to identify lost books), she had to bring that specific computer around the room in a cart. Such inconveniences are not insurmountable, but they're nice to get rid of. You don't need to back up a cloud service and it's available everywhere, even on smaller devices like your phone.
There's an intermediate level of convenience. The school did have an IT staff (of one person) and a server and a network. It would be possible to run the library database locally in the school but remotely from the library terminals. It would then require the knowledge of the IT person to administer, but for the librarian it would be just as convenient as a cloud solution.
I think the 'more than one user' alternative to a 'single EXE on a single computer' isn't the multilayered pie of things that KronisLV mentioned, but a PHP script[0] on an apache server[0] you access via a web browser. You don't even need a dedicated DB server as SQLite will do perfectly fine.
> but a PHP script[0] on an apache server[0] you access via a web browser
I've seen plenty of those as well - nobody knows exactly how things are setup, sometimes dependencies are quite outdated and people are afraid to touch the cPanel config (or however it's setup). Not that you can't do good engineering with enough discipline, it's just that Docker (or most methods of containerization) limits the blast range when things inevitably go wrong and at least try to give you some reproducibility.
At the same time, I think that PHP can be delightfully simple and I do use Apache2 myself (mod_php was actually okay, but PHP-FPM also isn't insanely hard to setup), it's just that most of my software lives in little Docker containers with a common base and a set of common tools, so they're decoupled from the updates and config of the underlying OS. I've moved the containers (well data+images) across servers with no issues when needed and also resintalled OSes and spun everything right back up.
There's an intermediate level of convenience. The school did have an IT staff (of one person) and a server and a network. It would be possible to run the library database locally in the school but remotely from the library terminals. It would then require the knowledge of the IT person to administer, but for the librarian it would be just as convenient as a cloud solution.