I think typically when we think of a sandbox game or MMORPG, we might FIRST think of a box with sand in it, and a kid playing with the sand, maybe using a shovel to make sand castles, or playing with a bulldozer and dump truck. Nobody is telling the kid what to do. The sandbox is mostly a blank canvas, although it doesn't necessarily have to be blank. A sandbox could really be anything where we create something, mostly independently
I think to create my own inhouse definition, I'll start here:
1) Making or tinkering with things, mostly independently
2) Generally what's created or made will somehow be visible to other players, just as a child in a sandbox will make something and other people nearby will be able to see it; in fact that can be half the fun--showing off your work!
So I don't think a sandbox is only defined by playermade cities or playermade houses or farms, or player-terraformed terrain. It's not necessarily something we do directly to the world. That is looking at a sandbox too literally; taking the sandbox analogy to extremes. Instead it can apply to character development, or items or even how we go about discovering the world.
Being able to choose the skills, stats or abilities you will train is important for something to be sandboxxy. It's a creative process, something you do mostly independently. You're in the process of manifesting your destiny. Do you like to be a fighter? Do you like to be a magician? Do you like to be both? Do you like instead to be a cunning rogue? Or something else? This is up for you to decide. The skills, stats and abilities are your sandbox. You take the tools you have and you tinker with them until you have created something you're happy with. The results are visible to other players because they can see your abilities in action. Granted, the choices you make are not completely independent, but it's hard for things to be truly independent unless we're truly creating them on a blank canvas, absent of any external pressure or stimuli. Even a sandbox itself implies we'll be making something like sand castles or hills of sand, so not even that is a blank canvas.
Evenso, not having strong directing forces when making decisions is a major component of a game being sandboxxy. If there was strong direction, the sandbox analogy could no longer apply, and neither would the process be fundamentally creative. Players need to have strong independence for this to be so. Considering travel for example, if there's really only one logical path, and it's nearly impossible to miss, it cannot be sandboxxy. If other players cannot somehow see the results of your travel decisions, it's likely not sandboxxy either. This can apply to ANY system in a game, not travel alone.
Ok, I don't want to make this post too long, since I want to try SWTOR tonight (for the first time!), so why do I like sandboxxy games or MMO's? This something I've labored over ever since I figured out I like open world games and competition, and don't like to be told what to do in games, neither do I like to be overburdened with quests or storylines--and most of all, I like to attempt to be unique in everything I do. It's a lot like spaghetti trying to unwind it all so I can make sense of it. But I'll try to answer this question below.
I like to tinker and rollover things in my mind. I earnestly mean this. I've always enjoyed to tinker with game systems, be they character development, my inventory, a strategy against my opponents, the items I'm using or something else. And I like to feel like I'm making my own decisions. I guess I'm a bit like a clumsy inventor, who really doesn't like to be told what to make or how to make it. I usually invent garbage, but it's the process itself I enjoy, not necessarily the results. (This is why it's so difficult for me to enjoy guilds. Too oftne joinng a guild just results in them telling me what to do and how to do it. I do not enjoy that. A good guild understands its members need space. Don't answer questions they don't ask. Let them enjoy the process of making mistakes and learning from them.)
A game isn't fun, and generally doesn't feel sandboxxy, if somehow: a game ends up feeling like I am not making my own decisions, it's not open ended, it's not competitive, has a lot of story (in the form of voiceovers, dialogues or text), I'm not unique, I'm not making lots of decisions.
But why? I'm not sure any of the above answers this question. If I had to answer teh quesiton in as few words as possible, and had to answer fast, I think I'd say I like sandboxxy games or MMO's because it's creative and feels like the sky is the limit. That doesn't answer everything about what kind of games I like to play, but in terms of sandboxes, it goes a long ways.
EDIT: And why SWTOR? It's not sandboxxy far as I can tell. It's not particularly challenging or competitive either. I think the reason I'm trying it is because I always hated on WoW and WoW-clones. I've played soooo many ffa PvP open world MMORPGs, I feel like I can't fairly rally against the kinds of MMO's I don't like unless I actually play them. I've tried a few mainstream MMORPGs, like DDO, EQ2, Neverwinter and maybe a couple more. This is an experiment. Maybe I want to figure out why people like these kinds of MMORPGs, or maybe I just want to make better arguments in the future.