The linked page has games in order according to number of games finished on GC, which is the closest we have to the inforation you asked about. But I don't think anyone's suggested using it as a kind of rating for games. One possible reason could be that the number of games played is quite small (CV's are a niche hobby!) except for the very most popular games (Shōgi, Chess, Sac, ⁊c.; only the first 15 games have over 100 games played) so statistical biases are quite likely; and the count doesn't take into account time, meaning that some games could have once been popular but now fallen out of favour, but would still show up with large numbers (I don't know how many, if any, this actually applies to in practice — probably it's unimportant with the small sample size anyway).
The linked page has games in order according to number of games finished on GC, which is the closest we have to the inforation you asked about. But I don't think anyone's suggested using it as a kind of rating for games. One possible reason could be that the number of games played is quite small (CV's are a niche hobby!) except for the very most popular games (Shōgi, Chess, Sac, ⁊c.; only the first 15 games have over 100 games played) so statistical biases are quite likely; and the count doesn't take into account time, meaning that some games could have once been popular but now fallen out of favour, but would still show up with large numbers (I don't know how many, if any, this actually applies to in practice — probably it's unimportant with the small sample size anyway).