To create a game video, you will need to follow three steps.
Edit your game footage. You will want to select the parts of your game footage that match the script you will follow when presenting the game in class. This will mean cutting and combining the relevant parts of your video.
For those looking for a more powerful solution that's still free, DaVinci Resolve has an excellent free tier.
If you don't mind spending money, consider Adobe Premiere, which is available at a discount for students. FinalCut Pro for the Mac also has a student pricing (but on a mac, stick with iMovie - it will meet your needs for this course).