From the headline one would think that this is the "secret ingredient" to the Roman concrete: "The lime was hydrated — incorporating water molecules into its structure — and reacted with the ash to cement the whole mixture together"
However, this is pretty much how portland cement (the modern binder in concrete) reacts with water to form the concrete with the agregate. Reading the article, however this is what matters:
"One is the kind of glue that binds the concrete’s components together. In concrete made with Portland cement this is a compound of calcium, silicates, and hydrates (C-S-H). Roman concrete produces a significantly different compound, with added aluminum and less silicon. The resulting calcium-aluminum-silicate-hydrate (C-A-S-H) is an exceptionally stable binder."
"At ALS beamlines 126.96.36.199 and 188.8.131.52, x-ray spectroscopy showed that the specific way the aluminum substitutes for silicon in the C-A-S-H may be the key to the cohesion and stability of the seawater concrete."
"Another striking contribution of the Monteiro team concerns the hydration products in concrete. In theory, C-S-H in concrete made with Portland cement resembles a combination of naturally occurring layered minerals, called tobermorite and jennite. Unfortunately these ideal crystalline structures are nowhere to be found in conventional modern concrete."
"Tobermorite does occur in the mortar of ancient seawater concrete, however. High-pressure x-ray diffraction experiments at ALS beamline 12.2.2 measured its mechanical properties and, for the first time, clarified the role of aluminum in its crystal lattice. Al-tobermorite (Al for aluminum) has a greater stiffness than poorly crystalline C-A-S-H and provides a model for concrete strength and durability in the future."
So basically, there is alimunium in the crystaline structure of Roman cement that contributes to the differences in performance over time (not raw strength). Another factor that may impact durability that is not covered here but that civil engineers will know well is the fact that modern cements are more alkaline than even early Portland Cement productions. As a result, they tend to react with the silicates in the aggregates of the cement (phenomenon known as alkali-aggregate reaction). If you see concrete with cracks that look wet even when it's not raining, that's a symptom of this effect. The reaction with the aggregates causes an expansion within the concrete which builds ups stresses locally and result in those cracks, with obviously unfortunate effects on the longevity of concrete structures.