Steam allows you to put games on any drive you want, so theoretically that should work, although I haven't tried it with thumb drives in particular. If the cafe allows you to, it would probably be best to download and install Steam and Slime Rancher into a USB drive from your home pc, and then just run Steam and Slime Rancher off of that USB drive in the internet cafe, so that you don't need to re-download them at the cafe. If you manage to get Steam and Slime Rancher installed on a cafe PC, then the cloud save mentioned above will allow you to continue playing where you left off, without needing to screw around with save files. In theory that means you can play this (or anything else) in the internet cafe, except that the cafe may or may not allow you to download steam and then a game like Slime Rancher that's up to the cafe and their policies. It is possible to play any of your steam games on any PC that has steam installed and you logged in to steam and has the game downloaded.
This is more common than not for steam games in recent years, and most people consider this a big positive. If you look at the store page in the right hand column, it says it uses cloud save, so the game save data is on a steam server backed up by steam, not in your C drive.
