I would do as Omnikuken suggested and go into your GenesisOrder in www/movies folder and try to play a video from there first. If it doesn't play then download a video codec pack and it should be fine. Windows does not have preinstalled allot of codecs that are widely used because of source code licensing and need to be installed through programs like K-Lite or other programs that contain those video codecs.
If it does play then there is another reason, heats not it. If heat was the issue, your laptop would shutdown and not simply give you an error and crash your game.
At that point, and I know this sucks, I would suggest trying to download the full game, not the update or compressed version, and try that. If you use a download link with a per day file limit, make sure you have enough left so that it does not have to pause and resume later.
Using a laptop, heat is always a concern, so clean it regularly and it should not be an issue.
You could deep clean it, take the heatsink off and replace the thermal paste, but that's something you need to either take to tech or you can do it yourself (videos all over youtube) just be careful they're easy to break.
As for needing to upgrade your laptop, that's hard to tell without the laptop specs like model #, cpu, and gpu information.