Migrating a Win32 app the way they suggest is going to be painful and time consuming. In addition, there are numerous things that they don't mention, like associated performance costs: is creating a thread going to be more expensive or cheaper on Linux vs. Win32? Don't look to the article for the answer. It doesn't even mention the biggest parts like the graphics/windowing library.
Secondly, it is making a wild assumption that your win32 app is written in a that is conducive to a Unix/Linux process model. Namely that you spawn processes and use environment variables as opposed to having a message loop and handlers (the way most windows apps are written).
Third, if it was so straight forward to port a Win32 app, why not just write a library that maps the windows calls onto the equivalent Linux calls instead of manually changing all your source?
Finally, why not look at a binary solution like Wine first and not touch your source at all?
This is the worst way migrate app. The source works and manually mucking with it like this is a good way to break it and introduce all sorts of bugs. Look for a binary solution like Wine. Then look to see if somebody implemented a Win32 on Linux library next to recompile (like Cygwin in reverse). Then, the last choice is to factor out your platform specific portions of your code and replace them with OS neutral calls. But beware of the performance of your app, it will probably take a hit. But, hacking apart your app like this makes me cringe.