Sorry but no.
All this statistics does is show the win ratio for all factions and that's it. You can't read game balance from these statistics due to the fact that although the size of the samples is equal, you can't guarantee that quality of these samples is equal as well. Top 200 of OKW players maybe be slightly more skilled than first 200 of USF players. What's more you can't even provide that each match will be against equally skilled opponents all the time because auto match will expand its brackets when no suitable opponent is found within specific period of time. I fought against JellyDOnut once and I don't have to tell you how this game ended due to skill level difference between us. It is quite common to get lower skilled opponent in a match up and it's quite common that your opponent will be much more skilled. The number of equal games I had is quite low. I am pretty sure it's the same when you're top 200. Maybe you get less skilled opponents more often because 200 players that's not that high number and they won't be able to play any games at all if match making only paired them against other top 200 player every time.
Also you can't guarantee that none of this data wasn't affected by balance differences, for examples maybe OKW win ratio would have been much lower if it wasn't for over performing Obersoldaten or Kubel Wagon, etc.
What we have here is a classic example of interpretation of the data to suit your need. First thing they are going to warn you against on every Statistics lecture.
Edit:
One more thing. Test sample is not even big enough to safely draw any conclusions.
Except it is, there is a reason statistic samples do not need to have thousands upon thousands of numbers to be accurate. As long as you have a sample that is correct enough (which this is). If the top 200 are not accurate enough for you, then your samples will never be good enough unless you take the whole population. It is highly unlikely that the majority of the OKW players are just all strait up better than all the allies players, the same could be said of when the Soviet win loss ratios were out of control
The sample quality is fine here, you could take a larger sample size and the results would not change very much (because this sample was chosen adequately).
It seems you want the sample to be absolutely perfect, which is absolutely absurd