The "file" version of a Google document, slideshow, spreadsheet or drawing is really just a fancy link to the online verison. You won't be able to carry around the latest sync of (desktop) Google Drive and open those as though they were actual files with real contents (except in the few cases were you exported a PDF, html, or rtf version of the file, and then that's not going to stay in sync with edits).
You can work with these files offline with the right Chrome app though.
You will need to install the Chrome browser, and then use the Chrome web store to install one of these apps.
- Google Drive
- Google Docs
- Google Slides
- Google Sheets
- Google Drawings
Look for the tag "Runs offline" in the details of the app, there's a few more that do, like Google Photos.
You do not need to install the desktop version of Google Drive to work with these types of Google documents/slides/sheets/drawings. You will then open each of these apps while online and allow it to sync at least once. Later you will find that you can open the apps and work with the synced files even if you are not connected to the internet later on. If you can't find the apps as the icon has moved around a few times, within Chrome they're at: chrome://apps/
Now the problem with this is that it requires you setup the target PC while online, possibly you'll be doing this setup repeatedly. Chrome profiles help a little here, in that you can setup these apps in your synced profile, then add a profile to the public PC, and when online sync it, then open those apps. You can work with them even if it goes offline, but you will need it to go online again before you leave the PC to sync the changes. Once you're ready to walk away you should delete the profile.
Alternatively you might be able to walk up to a PC with a portable version of chrome on a drive, but the issues section seems to indicate that profiles, settings, and extension state are now encrypted in a machine specific fashion probably rendering this unworkable.