As Death mentions his own interests, how does this support the idea that Death's point of view matters to the overall power of The Book Thief?

Yes, it is Death, our narrator (and a very pertinent character), that you are asking about; however, death is also the overall theme of the novel.  The dual nature of Death/death, then, shows the power of point of view in regards to The Book Thief.

Death’s interests often involve Liesel, one of the few people who Death takes notice of when he arrives to collect Liesel’s brother’s soul.  Liesel, of course, is absolutely terror-stricken...

Yes, it is Death, our narrator (and a very pertinent character), that you are asking about; however, death is also the overall theme of the novel.  The dual nature of Death/death, then, shows the power of point of view in regards to The Book Thief.

Death’s interests often involve Liesel, one of the few people who Death takes notice of when he arrives to collect Liesel’s brother’s soul.  Liesel, of course, is absolutely terror-stricken due to this death.  Liesel’s brother dies in her arms.  At the beginning of the novel, though, we are also told about the procedure of collecting souls from bodies (which is more Death's “job” than his “interest”).  I can certainly reveal something that does not interest Death:  “mystery.”  This is the reason why Death immediately reveals that Liesel’s friend Rudy will die in a bombing raid.  Further, as time goes on, Death needs a “mop” and a “broom” in order to clean up all the souls he must collect.  Obviously, so many people are dying in Germany during World War II.  Death reveals this to us by another one of his interests (which we should already know about):  his diary.   It is this diary that reveals Death’s distinct point of view.

In conclusion, one must understand how Death is not only a character but also the major theme.  Death surrounds everyone in Germany during World War II.  Jews die in concentration camps, on trains headed there, and in homes where they are hiding.  Non-Jewish Germans die if they are caught hiding Jews or caught with communist connections.  Any German could die at any moment due to the bombing raids by the Allies, especially as the war progresses.  The character of Death is everywhere just as the theme of death is everywhere in The Book Thief.