Norman Rafferty
Hipsters aside, I'm going to agree with Ebyan here -- "indie" means "not backed by a major publisher."

The simple way to answer the question is, if THE PRODUCT'S DESIGN DECISIONS answer to anyone else but THE CREATORS AND THE AUDIENCE, then you're no longer indie.

Did you get your budget from a publisher? Not indie.
Do you have stockholders who demand a profit, but who contribute zero content? Not indie.
Does all your money come from crowd-funding? That's indie, because the only two people involved are the creators and the audience. All decisions about the content will be INDEPENDENT of any other sources.

By this definition, Valve Software is an indie publisher. They're privately held, and only they and their audience decide what goes in them.

A great example of NOT-INDIE would be "Assassin's Creed: Unity". Many people were complaining, "Why can't I play a female avatar in this game?" And the answer was, "It's too expensive." In this case, expensive meant that the would have had to have produced twice as much cash-shop DLC, on the budget handed to them by the publisher.

The AC:U staff replied to the question in a way that showed no INDEPENDENT thought. They had a mandate from their bosses for so much content, they had a budget, and there wasn't room for women in it. There was a glaring lack of self-awareness in their response.

The indie label certainly implies someone's not a sellout... but one only has to browse Kickstarter to find people making steampunk-zombie-retro games. While an artist beholden to no one but a customer is definitely an independent artist... they can also still be a sell-out. Flappy Bird is not some kind of political or artistic statement.

Sure, a sell-out artist is making decisions about content to pander to a large audience, but they can still be an indie sell-out artist. There have to be at least two parties involved here; content has to be appreciated to be considered art.

The fewer people you have to respond to, the more indie you are. The MOST INDIE EVAR game is the game made to please only one person in the universe -- its sole creator. That's great for that one person, but when people think of art, they think of something to say something to an audience. Could be a large audience, could be a niche one, but it's got to have something to say to somebody.