What that actually means is that if the observations are representative of the underlying reality, then 1% of happiness is explained by playing video games. We

What that actually means is that if the observations are representative of the underlying reality, then 1% of happiness is explained by playing video games. We use p-values to determine whether a relationship is likely to actually exist based on observations. R^2 is a measure of the "strength" of the relationship, i.e. how much of the dependent variable is explained by the independent variable -- it is silent on the matter of whether the relationship is likely to actually exist.