In theory, 'storeyed' is an adjective and 'storey' is a noun.
It is a three-storeyed house.
'Storeyed' is describing the house.
As a compound adjective 'three-storeyed' would usually be considered to need a hyphen, but it's a rule that can be flexible, as we see in your example. 'Storeyed' is almost always going to be preceded by a number, so it is not as if there is much ambiguity to the meaning.
In practice, my experience is that 'storey' is used extremely commonly as both a noun and an adjective.
It's a thirty-storey high-rise. (Adjective)
The high-rise has thirty stories. (Noun)
In fact, I did not even realise that 'storeyed' was a word that existed in the context of the floors of buildings (in contrast to, say, "he had a storied past").
I think, therefore, the Cambridge dictionary is simply suggesting either version is acceptable. I'd add that 'storey' is a lot more common in the parts of the world I'm familiar with.
See examples here (North American) and here (British).
Perhaps 'thirty storey building' could be considered a noun phrase, in which case, 'storey' could be argued to still be a noun and not an adjective? Others are more qualified than me to say, and being part of a noun phrases does not remove an adjective's obligation to behave like an adjective. Whatever. In practice, the bottom line is that 'storeyed' is not common in my experience.