I don't know about that Ruby/Gem, but your app registration is not correct.
You need to configure your app for explicit OAuth2, per this other answer, except enter localhost instead of example.com.
(The localhost is based on the original version of the question. If you have a registered domain, use that.)
Then, in your ruby code:
I get the reason:
Do not use gem 'omniauth-stackexchange', '~> 0.2.1' ,but instead of gem 'omniauth-stackexchange', git: 'https://github.com/nashby/omniauth-stackexchange.git'
The reason see this:add call back url
I think you may be interested in these 2 methods:
/me (user): https://api.stackexchange.com/docs/me#order=desc&sort=reputation&filter=default&site=stackoverflow&run=true
You can access the user's reputation quite easily from there.