Is R2 score a reasonable regression measure on huge datasets?
The coefficient of determination $r^2$ is defined in terms of variance: it is the proportion of variance in the dependent variable that is explained by the independent variable. Variance is a property of normal distributed data. Hence, the coefficient of determination can only be used when you assume that  both the dependent and independent variables are normally distributed.

Just like other properties of normal distributed data, the estimation of $r^2$ improves when the amount of data increases. With very little data a coincidental colinearity might be the case, but this is not possible with large amounts of data.

Back to your example. Your data is cleary not normal distributed, it has right-skew and has large outliers. For this reason it is not advisable to use   $r^2$. Imagine for example that in the lower left corner (where the majority of the data is) you would observe a negative trend, but in general there is a positive trend. The regression line would be the same and the $r^2$ would be in the same range. This is known as the Simpsons paradox. 

In short, if your data is normal distributed you can use $r^2$ for any size of dataset. If it is not normal distributed you cannot use $r^2$.