> How do you realistically quantify someone's "overall happiness in life" and "burnout risk" into 1 number ?

There's existing survey methodologies for these, and then they added a Mario-specific set of questions (IMO these questions were poorly designed, they expected people to be able to accurately report how much Mario games specifically change their childlike wonder, which even if true, kind of changes the conclusion they should be able to make).

> I'm not sure how they did the control group

It's not that kind of study. They didn't sit half the participants down with Mario and half took a nap, it's interviews and surveys. Their only "control" was showing it didn't correlate with gender.