As was stated in the link Upsydaisy provided, the short answer is NO. Yes, you can install the Steam Client, but even then you will need to be able to run an Android or Linux app. But, no a cheap Chromebook will not be able to run any games. You will need to spend north of $600 for one that can run even low end games. And you have to be sure the game is able to be run on a non-Windows or Mac platform. Very few are.
Forgot to address the Netflix and Prime question. Yes, but as these are streaming services, this assumes you will have WiFi available during your flight.