You are correct, streaming videos is way more intensive. It's a couple gigs of data versus a few megabytes.
That's because when you watch a video online, you stream the entire video.
When you play a game online, the game runs locally, it just sends small data packets back and forth to update player position and npc AI.
I used my mobile data to play online games before I got a router and internet in my new house. Even an all-day 8 hour binge didn't noticeably effect my mobile data.
Video streaming like Netflix puts on thousands of times more load than gaming.
That being said, I don't necessarily think anyone should restrict their internet usage out of a sense of goodwill. No one will listen to the regulations anyway. Game or stream videos as much as you want. The system will handle it, or it won't.
Last night I re-installed a bunch of old offline games from my childhood and teenage years in case the internet starts cracking.