Your observation that the NIV capitalises the word “Abyss” is interesting, because none of the other Bible translations I have looked at say “Abyss”. Instead, they refer to “the bottomless pit”. Examples:
Revelation 9:11 NWT: They have over them a king, the angel of the abyss. In Hebrew his name is Abaddon, but in Greek he has the name Apollyon.
Revelation 9:11 KJV: And they had a king over them, which is the angel of the bottomless pit, whose name in the Hebrew tongue is Abaddon, but in the Greek tongue hath his name Apollyon.
Revelation 9:11 ESV: They have as king over them the angel of the bottomless pit. His name in Hebrew is Abaddon, and in Greek he is called Apollyon.
Revelation 9:11 NLT: Their king is the angel from the bottomless pit; his name in Hebrew is Abaddon, and in Greek, Apollyon –the Destroyer. Notes: The king of the locusts is identified in three ways: (1) as the angel from the bottomless pit (probably different from the fallen star, in Revelation 9:1, who unlocked the abyss rather than coming from it); (2) as Abaddon (“destruction”), often paired with death (see Job 28:22; Psalm 88:11), and (3) as Apollyon – the destroyer (see 1 Corinthians 10:10). There is also a connection with the Roman emperor Domitian, whose patron god Apollo was symbolized by the locust.
The NIV capitalises the name “Abyss” in Luke 8:31 and in the 8 places where the name appears in Revelation. In Romans 10:7 it uses the expression “the deep”.
The NWT uses the word “abyss” in Luke 8:31, Romans 10:7, Revelation 9:1, 11; 11:7; 17:8; and 20:3. The word is never capitalised.
The KJV uses the expression “the deep” in Luke 8:31 and in Romans 10:7. Elsewhere, in Revelation, the KJV uses the expression “the bottomless pit”.
Given that the NIV appears to be the only translation that capitalises the word “abyss” perhaps we need to find out why the NIV says “Abyss” when other translations say “the bottomless pit.”
As has already been pointed out, a person’s name (such as Abaddon, Apollyon, Domitian, Apollo) demands capitalisation. Places that are not proper nouns, such as “the bottomless pit” or “the deep” are written in lower-case. It therefore seems reasonable to apply that rule to “the abyss”.
Likewise, to say “the angel” is correct. If the Bible gives a name to an angel (for example, Michael or Gabriel) then it would still be correct to say “the angel Michael” or “the angel Gabriel” because there are millions of angels. Angels are not unique. But names are.
Why the NIV is the exception to that rule concerning "the abyss", I cannot say.