Perhaps it's better to start with the "what is not Chazzanus" question. This new video is a good example of pseudo-chazzanut, although it's actually sung by a Chazzan. Take a look:
Well, this is not Chazzanus. Helfgott's famous song Kanei is also not Chazzanus. Both these songs are an attempt to sing conventional Jewish Music in a Chazzanus way. Not by coincidence, they are both composed by Yossi Green, who loves to explore new styles and compose Pop Jewish Music with a hint of something else. Think Ki Hatov by Shwekey, a Sephardic song that is not Sephardic.
Chazzanus per se is ruled by Nusach, a set of moods, styles and singing techniques that are omnipresent in all great Chazonim and classical cantorial hits. The Nusach, combined with pieces found in Siddur prayers, is what sets Chazzanus aside from other musical styles, and is what gives this niche a life of its own. Nusach is the canvas that allows different Chazzonim to create new songs and improvise according to what they feel.
However Nusach is something difficult to master, and few Chazzonim today have this knowledge. Many know singing techniques and how to read notes, but few have the capability of innovating and composing new songs within the realm of Nusach.
The more you listen to the Golden Age chazzonim, the more you will understand what Nusach is. Look at what Wikipedia says:
The whole musical style or tradition of a community is sometimes referred to as its nusach, but this term is most often used in connection with the chants used for recitative passages, in particular the Amidah.Shlomo Carlebach used to say that the melody we sing in Yamin Noraim while starting Maariv and Hamelech in the Shacharit come from the songs of the Leviim in the Beis Hamikdash. These specific melodies are "Nusach", the standard way of reciting these prayers, and perhaps that is a colorful way of explaining where Nusach came from.
Many of the passages in the prayer book, such as the Amidah and the Psalms, are chanted in a recitative rather than either read in normal speech or sung to a rhythmical tune. The recitatives follow a system of musical modes, somewhat like the maqamat of Arabic music. For example, Ashkenazicantorial practice distinguishes a number of steiger (scales) named after the prayers in which they are most frequently used, such as the Adonoi moloch steiger and the Ahavoh rabboh steiger. Mizrahi communities such as the Syrian Jews use the full maqam system.
The scales used may vary both with the particular prayer and with the season. For examples, there are often special modes for the High Holy Days, and in Syrian practice the scale used depends on the Torah reading for the week (see The Weekly Maqam). In some cases the actual melodies are fixed, while in others the reader has freedom of improvisation.
Or in the words of Cantor Malovani:
Nusach is sanctified,” says Cantor Joseph Malovany, “just as the reading of the Torah is sanctified.”Malovany said it is extremely important for those who pray to become aware of nusach, the musical motifs that determine how one is to chant a given prayer.A classic song that highlights Nusach is Zevulun Kwartin's famous Tiher Rabbi Yishmoel, from Yom Kippur service. See below
A lot of this song is just reciting the words of this powerful piyut, but Kwartin manages to capture the essence of the words and create a song, which is sung in many shuls on Yom Kippur. If you want a more contemporary rendition of this song with full orchestra, see Chazzan Benjamin Muller's version, alongside Maestro Sobol:
Sometimes a Nusach song can be upbeat too, if that is the mood of the words being sung. But I will leave this for another post.