I really want to understand why Minecraft as a game is so popular, and get considered opinions on how a game that looks rather blocky, like it came from the early '90s, is so popular on this site. I was considering asking something like "Why do people play Minecraft?", but I don't think phrased as such, it would be very constructive question. It would probably invite flaming, and very short "big-list" type answers, which I know are against the ethos of Stack Exchange. Can someone help me rephrase my question so that I could ask it according to your community rules as to what constitutes a good question.
If you don't want to start by playing the game, then I think you should try out our chatroom. In particular, there's even a separate room for Minecraft. I'm sure people in the chat room would be happy to tell you their own experiences and thoughts.
The biggest issue I see for making yours a constructive subjective question is point #3 of the 6 reasons, which is what really threatens such questions for the "Subjective and Argumentative" close reason.
Great subjective questions have a constructive, fair, and impartial tone.
Your initial stance on the game, while we may understand you have no intent to slam the game, it puts players on a defensive side. I think using both the chat room, playing the game yourself, or watching a few videos (I recommend the chat room again as to ask for good ones) would be a great way to get some better footing in the game. Then, when you do come back to ask about it, you have a much more enriched perspective.
The other thing to consider is that ultimately, you want to keep the question out of being a discussion. Subjective is fine if it remains a question. If, by the end of your initial survey, you start to feel that there's no concluding answer to your question, then try to figure out what would change it towards that.
Personally, I have some trouble conceiving a viable form of the question you desire, because it is entirely rooted on an opinionated subject - what it is that makes individuals play a game. While there is the occasional fellow who may spite himself and continually play disliked games, all the more often this coincides with the reasons that such people like the game. This makes it extremely easy to attract answers which cannot be falsified. Trying to overcome this obstacle, I haven't even been able to find a good way that truly and effectively discourages opinion.
That said, PAX East, which I attended last month, did actually have a panel on exactly this - what it is that makes people keep coming to Minecraft. I missed the panel myself, but it's not to say someone else may have attended that panel, who can answer your question in the broad sense rather than on the personal sense.
I agree with Jeff's answer, with one caveat - you would have to pay (a relatively small amount of) money for the full game. There is a free Classic mode available, but it isn't the full game, and Survival mode is, IMHO, the best part. Hearing a zombie somewhere in a cave you thought you'd cleared and lit, is surprisingly disturbing...
The other thing you can try is ask the question on the Minecraft forums - which is not only a forum, and ideal for questions like this - but also guaranteed to have lots of actual Minecraft players.
As far as why people play... First, I think your categorizing it as a throwback is a mistake. For example, you can build a house in the game, out of materials in the game - how many AAA games can you do that in? Or build a castle, or a railroad system, or chop down a forest, or level a mountain if it's in the way of your railroad track, or...
As many people have said, Minecraft is a sandbox game, not a themepark game (google sandbox versus themepark game for more details).