You seem to have it about right. I'm not sure I would translate "finality" as "fatalidade", however, nor can I recall any specific Portuguese words that would precisely convey the meaning of "finality", which is quite abstract. "Conclusividade", perhaps?
As you have quoted, "finality" is the quality of being final. Shocking, I know. Jokes aside, it doesn't get a whole lot clearer than that. Something that is "final" represents a definite end and cannot be changed. This notion is described as "finality". Looking at examples and set phrases might help you get a better understanding of the word and its meaning.
The finality of death = The fact that death means a definite end to life and cannot be changed or stopped.
A sense of finality = A feeling that something has come to a definite end or conclusion, and can no longer be changed. Think of a court verdict, for instance.
To speak with finality = To say something assertively and conclusively.
The dictionary entries you provided offer some nice usage examples. You could also try searching for sentences containing the word "finality".