Playing games typically doesn't need super fast speeds. It's all about the speed and response to the server that hosting the game. When your actually playing a game the amount of date sent to and from the game server is generally pretty small.
Downloading games is a whole different issue. You want a fast speed to download a 50-100gb game, frequent game patches, windows updates.
Other services like streaming video also need a guaranteed minimum. For example it's recommended to have a 25Mb connection to stream Netflix in Ultra HD.
If it's available and affordable where you are then 10Mb is the absolute minimum download speed you want. If you can get it then 30Mb or more depending on your circumstances and usage.
I don't know about other countries but in the UK our regulator mandates that providers give both minimum speeds and accurate speeds. Accurate speeds are what you get at peak times - 8-10pm in the UK.
At the moment I'm only getting about 44% of my maximum upload speed due to so many people using the broadband in my area due to Covid 19.