Hmm... most people who won a medal at Rio 2016 won at most one medal of any color at the Rio Olympics. It's hard to tell anything just by looking at this. Intuitively, how height makes a difference (if one exists) varies by sport. You would expect that most successful gymnasts are shorter and most successful basketball players are taller. Let's look at a few sports!

There doesn't seem to be a big difference in height between medalist categories within each sport, but you can see a difference between heights of atheletes across sports (e.g. gymnasts are notably a lot shorter than basketball players). However, we are only looking at the median, which does not tell us the whole story. Let's take a look at the distribution of the points!

So, it appears that the distribution of points between medalists and non medalists is quite similar. So, being the shortest gymnast or the tallest basketball player does not mean that you will pick up more medals at the Olympics. But we can see that, for instance, gynmasts tend to be shorter than basketball players.