You're looking at an old version of the bill, Piob. The bill as passed by the House recognizes marriages performed by judges, as well (link to the passed version is below).
I'm actually a fan of the OK bill. I don't believe the state belongs in marriages at all, but their approach is a decent compromise. The state is basically saying, "fine, marry whoever you want. We're not going to be the arbiters of marriage anymore." I'm good with that.http://webserver1.lsb.state.ok.us/cf_pdf/2015-16%20FLR/HFLR/HB1125%20HFLR.PDF