Veteran said,
Yes you do. He is also called the king of Babylon,
Isaiah 14:4 ¶That thou shalt take up this proverb against the king of Babylon, and say, How hath the oppressor ceased! the golden city ceased!
And the king of Assyria,
Isaiah 10:12 Wherefore it shall come to pass, that when the Lord hath performed his whole work upon mount Zion and on Jerusalem, I will punish the fruit of the stout heart of the king of Assyria, and the glory of his high looks.
Daniel also has sevral names for the Assyrian and you probably know what they are.
You left the Scripture in question of Isaiah 30:31-33 which is SPECIFICALLY naming "the Assyrian".
I could easily go to many, many other Scriptures for other titles used symbolically to represent Satan in the end. And yes, the king of Babylon is another one of Satan's symbolic titles, as per Isaiah 14...
Isa 14:4-13
4
That thou shalt take up this proverb against the king of Babylon, and say, "How hath the oppressor ceased! the golden city ceased!
5 The LORD hath broken the staff of the wicked, and the sceptre of the rulers.
6 He who smote the people in wrath with a continual stroke, he that ruled the nations in anger, is persecuted, and none hindereth.
7 The whole earth is at rest, and is quiet: they break forth into singing.
8 Yea, the fir trees rejoice at thee, and the cedars of Lebanon, saying, Since thou art laid down, no feller is come up against us.
9 Hell from beneath is moved for thee to meet thee at thy coming: it stirreth up the dead for thee, even all the chief ones of the earth; it hath raised up from their thrones all the kings of the nations.
10 All they shall speak and say unto thee, Art thou also become weak as we? art thou become like unto us?
11 Thy pomp is brought down to the grave, and the noise of thy viols: the worm is spread under thee, and the worms cover thee.
12
How art thou fallen from heaven, O Lucifer, son of the morning! how art thou cut down to the ground, which didst weaken the nations!
13 For thou hast said in thine heart, I will ascend into heaven, I will exalt my throne above the stars of God: I will sit also upon the mount of the congregation, in the sides of the north:"
(KJV)
You are right in that Revelation 13 covers "two of the three beasts" of Revelations...The first is, indeed, The Kingdom of the Antichrist, but I fail to see how one could interpret "Satan as its king" as you argue? Satan has never wanted to be a "king" as far as I know.
Christ is our KING, and that's the Role Satan coveted from the beginning, i.e., God's Throne (see Isaiah 14).
Rev 9:11
11 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.
(KJV)
Also notice in Rev.11 a beast 'ascendeth' out of the bottomless pit to kill God's two witnesses. That can only be about Satan ascending from that bottomless pit, so that's a direct symbolic reference to Satan as a "beast".
That Rev.9:11 verse is about Satan as that "angel of the bottomless pit." Notice he also is a "king" according to that. Those are symbolic titles for Satan as Abaddon and Apollyon, which are most often translated as 'Destroyer'. Apollyon is from the Greek word for 'perdition', i.e. to perish fully, so that's another direct pointer to Satan, since only he and his angels have already been judged and sentenced to perish in the future lake of fire.
It's important to have first understood back in The Old Testament prophets how God told us specifically what sin Satan did against Him in the beginning that caused his fall. Ezekiel 28 is another Scripture which goes into that, as also Ezekiel 31, as it includes a direct reference to one who was in God's Garden of Eden. And we certainly KNOW that the flesh kings of Babylon, Assyria, Tyrus, Pharaoh, etc. were never in God's Eden. So it's a no brainer that our Heavenly Father was using flesh historical kings as types for Satan himself, for they all thought of themselves as gods in place of God too.