To address the summary, the difficulty is in proving certain security aspects, as current models don't fit the assumptions that RIBE models use. In practice, it could be fine.
The article seems to propose a set forward in a scheme to manage the keys by combining two previously proposed methods in a novel way. I can't judge if this is indeed an advance as I am not familiar with this domain. The main advance claimed is that the publicly needed parameters is constant. This suggests that other schemes had an issue in which the public information would keep growing as the number of issued keys and users grew, causing a scaling issue that limited practical, widespread applications. Again, I can't judge if this is indeed correct.
But, as noted, this does require a trusted third party to ultimately decide if a key is valid. Also, a lot of the work seems to be temporally based; the identity is combined with a timespan to create a key that is only use for a given set of time.
It's an interesting idea overall. It avoids the public key problem by making the information you need the channel in which you communicate on. (For example sending a encrypted email in which the key is the email address),