Do I need to redownload a game after downloading it on a USB?

[Shinryu]

I downloaded Spider-Man Remastered and I moved the steam files onto the USB stick, but when I tried playing it I had to re-download it. Is that supposed to happen?

[cSg|mc-Hotsauce]

Put it back and use the Storage Manager.

Steam > Settings > Downloads > Steam Library Folders

[Jaunitta 🌸]

If Hotsauce suggestion doesnt solve it

May I ask where did you move it to? And did use properties of game in library to move installation files?
Your downloaded game sounds like it is missing the steamapps files called acf appmanifest so steam needs to see them or the games appear as uninstalled.
If you can find that
Make a new folder on your USB name that folder Steam
inside place the game into a folder common
and before that make a new folder steamapps place asf file into that.

Exit Steam and then reboot go to Steam top left settings library manager add a new drive and make it default.

Just so know
When we move installation files Steam creates steamapps and common in the USB Steam folder.