I have to disagree with your definition of culture.

I think, in general, art is vital to a people's culture. More specifically, subcultures form around the creation and enjoyment of specific art forms - from graffiti to theater to, yes, video games. And those subcultures, in aggregate, form and inform a people's culture as a whole - because when people ask themselves what art is most important within a genre, what art most matters to their culture, what even counts as art and what doesn't - that determination is generally informed by the subculture that surrounds that genre of art.

When you're part of a subculture focused on a particular art form, and you aren't able to experience a work of art that people in that subculture consider important to experience, yes, you are missing out. Theater and movie fans have lists of shows every true fan needs to watch at least once. Fans of a particular musician would deeply regret missing their concerts when that musician is touring in their area. If gamers aren't playing the same games their fellow fans are, they'll be left out of discussions and won't understand the memes. And so on.

If you don't have the money or resources to do something that many other people in your subculture consider important, you are missing out, and it does suck. And this is true whether the thing being missed out on was created for profit or not. Because it doesn't matter why the thing was created. It matters how you and the other people in your culture feel about it.