This article seems to leave out a key caveat: They only proved this conjecture for sufficiently large n, not for all n. [Edit: Oops, apparently I was wrong, it does list that caveat -- but doesn't go into the further detail I discuss below.]
Now, if they have a bound on n, or if it's possible to derive a bound from their proof, then this could eventually become a proof of the full conjecture, by computer checking all smaller n. But if it's nonconstructive, then it can't be. To be clear, this is still an interesting and impressive result either way! But let's make sure we've correctly stated just what it is.
From the description in the article, it sounds like it ought to be possible to derive a bound on n from their proof. But from what I've seen, it doesn't sound like they've done so. So, now some proof-miner will have to go and do that for them, I guess, and possibly prove the full conjecture as a result...
Now, if they have a bound on n, or if it's possible to derive a bound from their proof, then this could eventually become a proof of the full conjecture, by computer checking all smaller n. But if it's nonconstructive, then it can't be. To be clear, this is still an interesting and impressive result either way! But let's make sure we've correctly stated just what it is.
From the description in the article, it sounds like it ought to be possible to derive a bound on n from their proof. But from what I've seen, it doesn't sound like they've done so. So, now some proof-miner will have to go and do that for them, I guess, and possibly prove the full conjecture as a result...