This whole site is community moderated. So, to answer your question, everyone is a moderator. We work together to establish a productive question and answer site. In order to do that, we must enforce rules established by the community in order to maintain a respectable level of quality.
I'm one of the pro tempore moderators that Pearson mentioned. For more information about their specific duties, check out this section of the help center. If you have an issue with any action I've taken, bring it up on meta and I'll be more than happy to discuss it with you.
..."Who decided on the moderators and what are their goals?" seems to have been misinterpreted, wholesale. The second part of the question - What are the goals of those that started and initially appointed moderators? If those goals have flex built in, and take consideration of the differences between those that design vs those that develop, then there's at least some room to consider what the possibilities are for adaptation to the realities of graphic design as hobby & profession.
I cannot speak on behalf of the goals of those that appointed me, started it, host it, or develop it. Nor was I even around when the first moderators were chosen for this site. I'm the newest moderator here, Pearson is the only remaining "first round draft picks". I fit none of those categories, but I can tell identify who they are.
Who appointed me?
I was chosen by the Stack Exchange community managers team. I don't know the specific details of the decision, but I can tell you it was Abby that made the announcement. She contacted me privately asking if I was interested and I accepted.
Who started this site?
You could say that Jeff and Joel started this site seeing as they're the co-founders of Stack Exchange, but that wouldn't be accurate. They merely provided the tools and the venue. This site was proposed as a potential site for Stack Exchange by existing users on other sites. The proposal required a group of interested individuals to come up with example questions and agree to commit their participation to the site. The list of 37 people that actively participated in the private beta can be found here, but those individuals don't have any special privileges.
Who hosts it?
Who develops it?
You can find the developers for Stack Exchange here
Is any of this relevant?
Not particularly. The founders and developers for the most part maintain a hands-off approach to our community. Internal periodical reviews are done by the community managers (employees of Stack Exchange) to make sure our site is doing alright. We are limited only by the technical aspects of the Stack Exchange platform.
So, who runs this community? The community runs this community. I cannot stress that enough. We aren't required to abide by any mystical "goals" of Stack Exchange. We are able to decide as a community what sort of questions should be on-topic at our site and which should not be. The scope of our site is not set in stone and is open to discussion and modification.
There are many aspects of our site that are against the rules at other Stack Exchange sites. I can give you a specific example: we allow software-recommendations. That is explicitly off-topic at Stack Overflow (and it's even one of the pre-cooked off topic close reasons).
If there's something specific that you think should be changed, bring it up. I will not dismiss anyone's opinion just because they are new to the site. All the same, I won't ignore the opinions of users that have been participating on the site for three years.
The goal of this community is to produce a high quality question and answer site. In order to maintain the level of quality that we expect, we cannot give carte blanche and allow any and all questions that are remotely related to graphic design. Our democratically chosen scope is focused on questions that are not too subjective or opinionated. Yes, that can be difficult when dealing with a subject like graphic design, but I feel we've done an alright job so far. If that restriction is too limiting for you, I suggest moving elsewhere.