Generally it seems like whether a player is a "main player" or a "supporting/complementary player" in the eyes of fans is whether they're good at scoring. In some respects, that's fair--as a solo star, you can't carry a team very well if you can't lead them in scoring. In other respects, that's not so fair--championship teams (almost) never consist of a single star, so the real question is how much you drive success in an ecosystem of two or three stars. I think Green is a "main player" in the overall success of the Warriors' run. He basically does everything (at least prior to this year) except be a potent scorer and has been a huge part of the team's defense (as the effective quarterback and all-court defender) and offense (as a facilitator).
This season seems to illustrate that Green is a poor choice as a solo star, but I think he remains a true star when he has other scoring stars on the team.