First, go into Get Info and change the Media Kind on the Options tab to tell iTunes that this is a video. Next, you need to sync this item from the Video tab on your iPod detail in iTunes (i.e. don't sync it as if it was a Music item). If you sync all video content then this will happen automatically once you change the Media Kind. But if you only sync part of your video library, make sure you include this video in the sync selection.
If you still have problems, you may need to convert the video for iPod playback, even if it plays fine in iTunes. If that's the case, right-click on the video and you'll see an option to convert for iPod use, which will make a copy (so make sure you know which version to sync to the iPod, or simply delete the original).