I am interested in building a piece of software for computers. I'm a web developer without much experience in the desktop game, so I'm probably going to hire this out, I just wanted to make sure it isn't a crazy deep project before I start because my development budget isn't that high.

The purpose of the program will be to report game activity of users back to my server (a gaming community website). Something similar would be GameTracker. Once you install the GameTracker program, it runs in the background and everytime you start a game up or close it down, it is reported to their server and this activity shows up on your profile. Example
Dan started playing Call of Duty
Dan stopped playing Call of Duty
Dan started playing Grand Theft Auto
Dan stopped playing Grand Theft Auto.

It would also be nice to add features to it in the future as needed such as a messaging/alert system that would alert users if they have new messages/alerts waiting at the website for them, like Origin, etc. has. The website is nearing completion and I need to start getting some of the other components ready for testing so any help is greatly appreciated.

The reporting and messaging is not difficult at all.
Identifying when a game is started or closed could be more difficult, depending on what the operating system is, and whether the games in question have any software hooks that you could use to monitor them.

The operating system would be Windows. I would hope to offer it on Mac later but initially it would be Windows only since a majority of computer gamers use Windows. Does that add or subtract from the probability/difficulty of getting it work?

Obviously you would want to use a cross-platform language for the communications etc, but the monitoring for game apps starting/stopping would presumably be completely different