I'm not sure we can assuredly answer this without turning to non-Scripture. This is an attempt through Scripture and reason only.
There certainly is reason to think that Angels enjoy immortality of some kind. Throughout the thousands of years recorded in the Scriptures, prophecy included, we continuously see the same Angels doing God's work, and those also working against God. Satan is in Genesis, whom we know is Lucifer, and he is also in Revelation at the end of days when he is finally cast into the Lake of Fire. Gabriel gave God's message to Daniel and later to Mary also over 700 years later. Michael was also there doing many things. It is, therefore, reasonable to assume that Angels enjoy immortality, but is it of the same sense that we first think, meaning is it inherent to their character, as given by God?
Although you clearly state to not hold this view, the Annihilationist perspective, in addition to claiming that there is no immortal soul, generally holds that immortal life for mankind is not inherent to his character, as given by God. It was actually the Tree of Life that sustained the human body through the ages (or was supposed to do so). By sustained I mean that the fruit from the Tree of Life was eaten regularly. This is supported by Revelation 22:1-3 where the leaves of the Tree of Life will be the healing of the nations and in Genesis 3:24 when it is clear that one of the main reasons to keep man out of the Garden was to keep him from eating of the Tree of Life. This alone does not necessarily contrast the view you request.
So from this reasoning we might say that the angels, evil and righteous, have access to a Tree of Life of some kind. An issue, however, is that Revelation 20:10 states clearly that the devil, the beast, and the false prophet will be tormented forever. If torment were easily relieved by death and angels' immortality was sustained by a tree of some kind then they would merely no longer eat it and escape the torment.
But for the perspective that you ask we may not be able to reason in the same way. In fact, what is common among mainstream Christianity is a redefining of the word death (in Genesis) to mean separation from God, rather than bodily death. So the question then becomes why does bodily death occur for mankind and seemingly not for the Angels, despite both having sinned?
The answer must be in God's redemptive plan for mankind. There appears to be no redemptive plan for the fallen angels and it seems that they still enjoy immortality. This is not a coincidence.
God is a God of great glory. All that he does is to His magnificent glory. From our limited vantage God granting immortality to the character of part of His creation glorifies Him greatly, and He is equally glorified that He overcomes death and resurrects all the dead to Glory with Him or damnation in the Lake of Fire. Romans 9 is very clear that God does all things for His glory, "that [His] name might be proclaimed in all the earth."
It is to God's glory that mankind perishes and his body withers to dust. It is to God's glory that angels, wicked and righteous, are immortal by His graciousness. It is to God's glory that the wicked angels will suffer lasting torment. And, finally, it is to God's glory that all mankind is restored to his body and given new life, new life for glory with Him or new life for destruction in the Lake of Fire.
We are above the angels, and even all of Creation. Mankind is the pinnacle of all Creation, meant to rule over it with only God above us. God, therefore, required more from us. For our failure to obey him we received death (bodily). More than that, God required continued bodily death for our continued sins in the sacrifice. Then finally, God receives the most glory in the sacrifice and resurrection of His only begotten son.
Without bodily death God could not receive the fullest glory due to Him that came from Christ's sacrifice and resurrection. Conversely, if angels also had a redemptive plan it would show that the angels and mankind are equals because Christ would not need to die twice, once for angels and once for mankind, for His sacrifice is eternally sufficient.