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Scientists Create New Material Five Times Lighter and Four Times Stronger Than Steel
(scitechdaily.com)
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If they are writing using proper materials terminology then strength tells you a lot, since it has a pretty rigorous definition: amount of energy absorbed before failure.
Which, given one of the researchers themselves is quoted talking about its strength, I'm guessing they are even unintentionally being more precise than you're expecting of them.
As for the properties: smaller sections being stronger is fairly normal amongst materials. The smaller a manufactured section, the more catastrophic any given defect will be. At a certain scale, you will be guaranteed to have either perfect, or already failed, material.