In my opinion, Milonguero is a status at the milonga that means veteran. They say you are a milonguero when you have been going to dance every night to several milongas per night for several years and you get a special understanding of the abrazo, the codes, the circulation (always forward), you don’t crush other couples, you don’t do bullshit steps, you listen to the music, you focus on your walking, you own your table at the best location at the best milonga, you have rituals, when you understand, respect and you are respected.
But it is not like you assert that you are a milonguero, it is more like people at milonga accept you like one of them. It is like citizenship of tango.
It means that other milongueros respect you.
When they tell you they are going to teach you milonguero style, it means that they are going to teach you real tango, not the bullshit they teach ay NYC, among other places.