I'm sorry, but i think this approach is a bit wrong, because it doesn't emphatize the fact that games with more votes have a more precise score. It's like saying that every game that has more than 10 ratings has a 100% precise score.
I think a Bayesian approach would have given a better result.
For example, the formula for calculating the Top Rated 250 Titles in IMDb gives a true Bayesian estimate:
weighted rating (WR) = (v ÷ (v+m)) × R + (m ÷ (v+m)) × C
where: R = average for the movie (mean) = (Rating)
v = number of votes for the movie = (votes)
m = minimum votes required to be listed in the Top 250 (currently 25000)
C = the mean vote across the whole report
I believe that, with the same formula, if we substitute m with the median (in this case 10), we would get a more accurate estimate of what the game score should be.