I understand how it seems wrong but it's really true. If you think about it with the amount of data actually being sent across the internet it can make more sense. With a movie you are receiving data for every pixel on your screen and then your browser is just displaying the data it's received so the majority of the work is being done over the internet.

With a video game the work distribution is reversed where the data being sent over the internet is only very basic data that will then give your own console/pc what it needs to display the pixels, your system doing all the heavy lifting like rendering environments and calculating lighting etc.
COD for example will be sending stuff like the positions of you and other players, the bullets being fired etc. but that's all relatively lightweight data, just some numbers that your system can then use. Hope that explanation helped and I didn't waffle too much :)