Well, the SC has the pattern: DM sets scene, player declares action, DM narrates effect and new scene, player declares action ... The 'effect and new scene' can quite easily be effectively a DM action declaration "the bad guy responds with X"
By "no action declartions" I was meaning that the GM doesn't engage the mechanics - s/he just says what is happening, and the burden shifts to the players.
It's not quite the same as "players roll all the dice", because in that sort of system the GM still makes a decision for the monster (eg declares an attack) - the "defence" roll in that sort of system is just like the traditional saving throw.
It's more like DungeonWorld, except I think even more free-form: the only constraint on what the GM describes as happening is the group's shared sense of acceptable fiction relative to genre, the current situation etc. So in the wild mine cart ride scenario )that I think I've seen you use a few times as an example), the GM is free to just state that "a rail has come loose in front of you" or "another car is careening towards you, out of its siding onto your track" or "sparks from the brakes look like they might set fire to your [widget]" or whatever else makes sense and will keep the pressure on. Contrast to combat resolution, where - unless it's a fudge-for-all - the GM can't just say "the giant's club is on a collision course for your head - what do you do?"
Other closed scene resolution systems that I'm familiar with tend to be more like D&D combat. BW is - and is mostly opposed checks; MHRP is always opposed checks, either against the Doom Pool or another character, and to introduce new adversity into the situation the GM has to spend resources to create a new scene distinction or scene complication, or to introduce a new NPC; HeroWars/Quest is always opposed checks, with the GM rolling with a bonus determined either by the opposing character or by an analogue of the DC-by-level chart (with pacing considerations as well as level factoring in: the more successes in a row the PCs have experienced, the bigger the GM's bonus on the chart).
One upside of the skill challenge approach, compared to these other approaches, is because there are no opposed rolls in a SC you can't fall into the lazy fun of "dice bingo": we can't just both roll and see whose number is bigger. Ideally, this means the GM
has to put effort into describing the fiction, and the player
has to explain how his/her PC is engaging that fictional situation in order to frame the check. (The ugly shadow cast by this is that if the GM turns the SC into bingo - "Who can make a skill check to beat DC X?" - then it is the most boring "bingo" ever, because you're not rolling against anyone else, just a static target number.)
One downside of the SC approach is that, by default, it can't handled PvP. The DMG2 had a clever example of how to adapt the system to a type of PvP, where the PCs are on different sides of a debate, and the first to get to N successes wins for their team. But that is still not
direct PvP (eg an argument between PCs). I don't think the SC structure can handle that.