It is based on the total number of pilots on the rosters, not the numbers in flight.  
The difference in the screenshots is the relative disparity between the lowest numbered country vs the other 2 respectively.  In one screenshot Rooks have a 12.3% advantage over the lowest country.  In the next, bishops have an 18.7% advantage and concequently have a higher ENY limit even though the percentage of the high countries are almost identical between the two screenshots.  In that same image, the rooks have a 15.3% advantage over the small country and are also subject to ENY limits.
HiTech posted the code for it in this thread
The code does not tell me what eny means, hence code.
However if you break down the numbers from each one, even though the percentages are fairly close, there is a dramatic eny difference.  Why?
I understand that ENY comes from players in country, not in flight.                
Country Cnt   Inflight Waiting   %Total Min-EnyExample 1. Bishops   178   127        0        28.5%    0.0
               Knights   192   139        0        30.7%     0.0
               Rooks     255    185       0        40.8%     3.7
Example 2. Bishops   72     44         0        40.7%    13.8
               Knights   39      31        0        22.0%     0.0
               Rooks     66      49         0        37.3%     8.4
Example 1 has a 40.8% and a 3.7 eny
Example 2 has a 40.7% and a 13.8 eny
Example 1. - 77 players difference, which imposes a 3.7 eny.
Example 2. - 33 players difference, which imposes a 13.8 eny
Nothing about this adds up to me and does not appear to be proportional.  
I would have thought that a stiff eny would apply to a 77 player advantage since a 13.8 eny is applied against a 33 player advantage.