How can I force a folder and the contents to be downloaded locally and not uploaded to the iCloud?
I have tried including a folder in the same location as the videos with .nosync in the name, but the files still upload.

But have you tried changing the name of the folder that contains the files to end with .nosync? iCloud Drive ignores the contents of folders named with .nosync, not the files that are in the same directory as such a folder. So, in your example, you'd change the name of the folder Lecture Videos to Lecture Videos.nosync.
Also—perhaps a simpler solution—you could simply move your Lecture Videos folder somewhere on your disk that isn't a subdirectory of ~/Documents or ~/Desktop, which are the two folders automatically synced to iCloud. For instance, you could put your Lecture Videos folder in ~/Pictures or ~/Downloads.
And, lastly, before you leave for your trip, you could go to System Preferences &gt; Apple ID &gt; iCloud and disable Optimize Mac Storage, which—if your laptop has enough free space—will (usually) prevent files from being automatically removed from your local disk once they're uploaded.