Pendrive/Thumbdrive question

Forgive me if I'm posting in the wrong forum, category, etc. I'm typing this on Linux Mint, which is pretty much the only time I've touched linux for more than 2 minutes if you don't count ChromeOS and Android. I had just learned how to boot from a USB (so I can use the family computer without using the family Vista) and it's running great.

Anyway, I notice that even though I have a 16GB thumb drive, I was only allowed to create 4GB of persistent space on top of the OS to save files and such. If I wanted to put Steam and Oblivion on here (upwards of 7GB in all), do I have to actually install Linux mint to the hard drive? Or is there a different software I should have used other than pendrive to create more writable space on this USB stick?

I'm merely experimenting at this point, but I'm always curious. Thanks!