From the perspective of a space elevator, it's not. Read this paper linked from the article. There's no talk of space elevators, that's just their way to entice the reader into listening to them.
That is to say, the space elevator mention is just clickbait.
As the paper notes, "experimentally measured tensile Young's modulus for SWNTs ranges from 320 GPa to 1.47 TPa with the breaking strengths ranging from 13 to 52 GPa". A material with the density of SWNTs is generally considered to need at least 100-120 GPa irreversible yield strength (less than breaking strength) to make a "practical" elevator (although if you read those proposals it's hard to come across with any conclusion other than that they're being way too optimistic even with those numbers). Note: 13-52 GPa for individual tubes. Ropes of multiple tubes are 1-2 orders of magnitude weaker.
So what about these diamond nanothreads?
The yield strength experienced more than 25% reduction (from ~ 75 GPa to ~ 56 GPa) for the DNT-14 when the sample length increases from ~ 13 nm to 26 nm. Afterward, it fluctuates around 56 GPa. Unlike the yield strain, the yield strength for all considered DNTs saturates to a similar value (around 56 GPa) and exhibits a relation irrelevant with the constituent units for the investigated length scope (fro ~13 - 92 nm)
Their data is pretty consistent, with graphs showing a clear dropoff and stabilization around 56 GPa. Obviously nm-sized fibers are pretty worthless for the purposes of an elevator, there'd be way too little Van der Walls holding them together into a rope.
Now, these are just simulations. But more often than not real world seems to underperform simulations rather than overperform, so I wouldn't get too optimistic about the real-world greatly exceeding these figures. For example, early simulations of SWNTs said they'd be around 120GPa; few believe nowadays that they can even approach those figures.
But what about the density side of the equation? After all, a material can be weaker, but if it's correspondingly lighter, then that's not a problem. The density is not in the paper, but this cites the tenacity (breaking strength over mass) as 4.1e10^7 N-m/kg. While the yield strength is going to be a bit less than the breaking strength, it shouldn't be too far off - this means that the density should be somewhere less than - but not too much less than - 1,37g/cm^3. That's on the same order as SWNTs, unfortunately.
Short answer? We're still nowhere even remotely close to being even capable of making a space elevator.
Space elevators face such numerous problems anyway (really don't want to have to go into them all) that they're really not a fruitful avenue of pursuit. We'd do far better to direct such efforts to more realistic access methods, such as a Lofstrom loop or variant thereof, which requires no unobtanium and is far more efficient (space elevators lose huge amounts of energy to transmission losses, throwing away a large chunk of the advantage that they gain from bypassing the rocket equation). Active suspension via recirculating kinetic transfer, by one means or another, is something we can do today.