So I got one C#/XNA game built in a class at college that I would like to add to my e-portfolio. The game works fine here with no compiling issues. However I would like to distribute the game through my e-portfolio without sharing the source code of the game.

I did some reading around online and it seems like I need to publish the game. In Visual C# 2010 Express I select "Build -> Publish <project name>" to build a setup.exe file to install the game. I tried installing this on another machine to see if it will work, and it seems like that machine would have to install XNA from Microsoft's server.

Would this be the best way to distribute my game? My e-portfolio is a blog that people can visit and download the games I made. I'd rather not just upload the entire project but just the game itself so people can play with it.

Unrelated to distributing your game, you should put videos on your portfolio. Most people won't actually download your game, but are more than happy to watch gameplay videos.