As you can probably see from the existing answers, the answer to your question is quite subjective and essentially boils down to one's epistemological perspective on the word "accurate".
My take is that the answer to your question depends on who the intended audience is and what the author's goals are. If the intended audience is people who know absolutely nothing about quantum computing, then (in my personal opinion) this is a defensible (although highly simplified) presentation for a first pass.
I very respectfully disagree with Craig Gidney's claim that "try every case" is "not at all how quantum algorithms work". It is certainly not exactly how quantum algorithms work, but it is something like how quantum algorithms work. Whether the analogy is close enough to be useful again depends on what your goals are. For an expert like Craig Gidney who is actually trying to discover or improve specific quantum algorithms, it certainly is nowhere near a precise enough heuristic to be useful. But for someone trying to explain an exciting new technology to a totally non-expert audience, I think it's a decent heuristic.
Craig Gidney and Martin Vesely (and Scott Aaronson as well) also suggest a specific claim that I slightly disagree with, although probably in a direction that's mostly orthogonal to their thinking. That idea is Craig Gidney's claim that the massive-parallelism picture "doesn't give any sense of what quantum computers are actually good at, and it doesn't give any sense of what they're not good at", or Martin Vesely's more specific claim that it implies that quantum computers could efficiently solve NP-complete problems (which is believed not to be the case).
I very respectfully suggest that that claim assumes that the median person who reads these descriptions has more of a "theoretical computer science" mindset than is actually the case. I suspect - and this is just a suspicion, I could be wrong - that for the median person who reads that description, the main takeaway is closer to "There are some problems that quantum computers can solve very fast" than to the more specific claim that "Quantum computers can efficiently solve all problems that would benefit from massive classical parallelization." And the former takeaway is completely correct. Note that my disagreement is solely on sociological grounds, not on any grounds of either computer science or physics.
More concretely: suppose you took the average person with no background in quantum computing who read that figure and thought "Okay, I kinda get that", and you asked them "Would a quantum computer be able to efficiently find the shortest path through a complicated travel network that hits every city?" I don't think that the person would confidently reply "Yes - the quantum computer would calculate the length of every path in parallel and extract the shortest one" (which would be incorrect). I suspect that it's more likely that they'd say something like "I have absolutely no idea. But I guess maybe it could use this crazy superposition business to solve the problem faster than a regular computer could?" (which, in my opinion, is not a bad answer for someone who realistically probably doesn't really need to know many more details that that).
The problem is that there aren't any great pedagogical alternatives to the "massive parallelism" picture that are useful to someone with zero background in QC and little interest in studying it formally. Framing quantum computing as a modification to the usual rules of classical probability is absolutely the best way to go - if you want to actually teach someone how it really works. But I don't think that's the goal of the Time magazine article - and frankly, I don't think that necessarily should be the goal, either.
I think that the "massive parallelism" story would be inappropriate to present in an undergraduate intro to computer science course, or even in a general-interest science outlet like Scientific American - it just isn't accurate enough. But I think it would have been defensible for Time magazine to present it to the general public, if they had added in a footnote saying something like "This is a highly simplified explanation that glosses over many important subtleties."