Well thanks for nerdsniping me. My prior query in the comments is limited due to the idiosyncratic conventions of the data explorer to return only 50,000 rows. In that query I got around this problem by only selecting users with a reputation over 1 (people who sign up for the site and have their account associated de facto get a rep. of 1). Apparently the Gini coefficient is pretty sensitive to how you treat these people though. If you plot the ECDF, just imagine keeping the curve at the same place, but stretching the X axis to the right by a large amount.
Here is a new query that hops around that problem, in which you can input where the cut-off in reputation scores is considered. Here is a table of our site compared with several others, varying the cut-off at -100 (which effectively captures everyone - ?is Gini OK for negative values?), the cut-off above 1 (so eliminates those browsers who just had the 1 point) and 100 (who can also be browsers if they have the 100 boost from a neighboring site).
Site >-100 >1 >100
Cross Validated 0.81 0.68 0.54
Stack Overflow 0.95 0.91 0.77
Mathematics 0.90 0.85 0.76
Theor. CompSci 0.64 0.45 0.41
GIS 0.82 0.74 0.60
You can see the Gini metric is pretty sensitive to these cut-offs. The more people you cut-off the more equal the sites become. These appear to agree with my prior post based on answers off-hand. Theoretical computer science is the most egalitarian, CrossValidated is in the middle with a few others, and Mathematics and Stack Overflow have the most inequality. (Others feel free to add sites to my table.)
Now, does this have anything to do with your questions? I'm skeptical it does.
Off-topic rant - it is common in ecological models in social science for people to put inequality scores (Gini or others) on the right hand of regression models and interpret them as "more inequality results in some particular outcome". I have a difficult time relating such inequality measures though (which are based on economic ideas such as egalitarian transfers of funds) to micro-level individual behaviors. Take for instance a really simple 4 person society, and try to write out how exactly changing the cash one person has to members of the group. Measures like Gini imply a whole complicated lot of functions that on their face seem at best over-complicated.
This is all academic though. I don't know how to encourage more users for the site - which is the whole point of the question. Talking about metrics like Gini as if they matter as an outcome is a bit red herring.
For those interested, the GINI measure I calculate is based off the formula on this website. For a more academic reference though, Paul Allison gives two alternative formula in the reference below.
Allison, Paul D. "Measures of inequality." American sociological review (1978): 865-880 | PDF Link