The links you presented in your question presents the Shito-ryu version of the Matsumura-no-Rohai Chu kata. The second link doesn't present other than a kata curriculum which mostly pertain to the Matsumura Seito system.
As most Shorin Ryu Kata, Rohai is share between schools of Shuri and those of Tomari. In fact, Rohai in different versions are accredited to different masters. Yes, there is Matsumora-no-Rohai (Tomari-te), as there is a Matsumura-no-Rahai series (Shuri-te), and there are modern versions devised by masters such as Itosu.
If you study carefully the different versions of Rohai you will find that the ancient versions all have a Chinese flavor in its technical aspects, as well as in its angles of movements; while modern versions all have movements that can easily be identify as of modern Karate-Do.
Matsubayashi Rohai is a good example of an old version, while the Chito-ryu Rohai series are evidently a more modern version. The technical complexity of the Matsubayashi version of Rohai when compared with those of Chitose, provide substantial evidence to compare the difference between ancient and modern versions of Okinawan Karate kata.
Rohai is originally a Chinese pattern, that was brought to Okinawa during the mid-1800Ās by several sources. Rohai is a pattern that was widely practiced in Fujian as part of the white crane systems of that province. Experts such as Wai Zing Xiang (Waishinzan), Ason, Iwah, Taitei Kojo, Sokon Matsumura, and several others, used to share knowledge and training sessions while in Fujian. The same happened in Okinawa after 1830, when several students, practitioners, and experts used to gather for training sessions and knowledge was shared without ego. It is not a forbidden fact that Tomari practitioners used to go to Shuri and train with their seniors and peers, such as the case of Kosaku Matsumora and Kokan Oyadomari, who shared training sessions with Sokon Matsumura.
At the present time, there are several different versions of Rohai kata, the Matsumura direct family lineage does contain 3 Rohai katas (Ge, Chu & Jo) which are not those of Itosu, while Shobayashi and other ryuha derived from Chotoku Kyan does preserve a different version of Rohai which is by some means similar to that of Matsubayashi.
Rohai is a kata that was brought to Okinawa by three different experts, Ason, Iwah and Matsumura; each taught the kata and the kata evolved into different versions in Okinawa and also later in mainland Japan.
One important fact that must be understood about ancient karate (Uchina-di or Okinawa-te) is that kata was taught differently to different students according to the skills and ability of each individual. This teaching principle is opposite to that of nowadays karate-do where everything is taught under a particular standard in a uniform manner. Therefore, in ancient times a kata could be performed differently by two students of the same teacher and they both were accepted as legitimate. This is the reason for nowadays each karate ryuha seems to perform the same material from different perspective and in different fashions.
If any adherent of Shotokan observes the particular angles of execution of Gichin Funakoshi and compare it with the modern JKA version of kata performance will notice that modern Shotokan is not exactly as Funakoshi used to perform. The same happens with modern Shito-ryu, Shorin-ryu, Goju-ryu, etc.
The importance of kata does not rely in a particular style of performance, but instead in the benefit said kata provides to the technical growth of the practitioner.
Hope this will help clarify some of the questions in regards to the Rohai kata.