And how do you come to this conclusion since Satan is never mentioned anywhere in the context?
The devil has many names such as serpent, dragon, man of sin, son of perdition, and many more. The assyrian is one of his names. If you read both of the chapters below, you will see that GOD is talking to lucifer, son of the morning and directly names him as the assyrian and speaks of his position in the Garden Of GOD, which is the Garden Of Eden and what he did.
Isa 14:1 For the LORD will have mercy on Jacob, and will yet choose Israel, and set them in their own land: and the strangers shall be joined with them, and they shall cleave to the house of Jacob.
Isa 14:2 And the people shall take them, and bring them to their place: and the house of Israel shall possess them in the land of the LORD for servants and handmaids: and they shall take them captives, whose captives they were; and they shall rule over their oppressors.
Isa 14:3 And it shall come to pass in the day that the LORD shall give thee rest from thy sorrow, and from thy fear, and from the hard bondage wherein thou wast made to serve,
Isa 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!
Isa 14:5 The LORD hath broken the staff of the wicked, and the sceptre of the rulers.
Isa 14:6 He who smote the people in wrath with a continual stroke, he that ruled the nations in anger, is persecuted, and none hindereth.
Isa 14:7 The whole earth is at rest, and is quiet: they break forth into singing.
Isa 14:8 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.
Isa 14:9 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.
Isa 14:10 All they shall speak and say unto thee, Art thou also become weak as we? art thou become like unto us?
Isa 14:11 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.
Isa 14:12 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!
Isa 14:13 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:
Isa 14:14 I will ascend above the heights of the clouds; I will be like the most High.
Isa 14:15 Yet thou shalt be brought down to hell, to the sides of the pit.
Isa 14:16 They that see thee shall narrowly look upon thee, and consider thee, saying, Is this the man that made the earth to tremble, that did shake kingdoms;
Isa 14:17 That made the world as a wilderness, and destroyed the cities thereof; that opened not the house of his prisoners?
Isa 14:18 All the kings of the nations, even all of them, lie in glory, every one in his own house.
Isa 14:19 But thou art cast out of thy grave like an abominable branch, and as the raiment of those that are slain, thrust through with a sword, that go down to the stones of the pit; as a carcase trodden under feet.
Isa 14:20 Thou shalt not be joined with them in burial, because thou hast destroyed thy land, and slain thy people: the seed of evildoers shall never be renowned.
Isa 14:21 Prepare slaughter for his children for the iniquity of their fathers; that they do not rise, nor possess the land, nor fill the face of the world with cities.
Isa 14:22 For I will rise up against them, saith the LORD of hosts, and cut off from Babylon the name, and remnant, and son, and nephew, saith the LORD.
Isa 14:23 I will also make it a possession for the bittern, and pools of water: and I will sweep it with the besom of destruction, saith the LORD of hosts.
Isa 14:24 The LORD of hosts hath sworn, saying, Surely as I have thought, so shall it come to pass; and as I have purposed, so shall it stand:
Isa 14:25 That I will break the Assyrian in my land, and upon my mountains tread him under foot: then shall his yoke depart from off them, and his burden depart from off their shoulders.
Isa 14:26 This is the purpose that is purposed upon the whole earth: and this is the hand that is stretched out upon all the nations.
Isa 14:27 For the LORD of hosts hath purposed, and who shall disannul it? and his hand is stretched out, and who shall turn it back?
Isa 14:28 In the year that king Ahaz died was this burden.
Isa 14:29 Rejoice not thou, whole Palestina, because the rod of him that smote thee is broken: for out of the serpent's root shall come forth a cockatrice, and his fruit shall be a fiery flying serpent.
Isa 14:30 And the firstborn of the poor shall feed, and the needy shall lie down in safety: and I will kill thy root with famine, and he shall slay thy remnant.
Isa 14:31 Howl, O gate; cry, O city; thou, whole Palestina, art dissolved: for there shall come from the north a smoke, and none shall be alone in his appointed times.
Isa 14:32 What shall one then answer the messengers of the nation? That the LORD hath founded Zion, and the poor of his people shall trust in it.
Eze 31:1 And it came to pass in the eleventh year, in the third month, in the first day of the month, that the word of the LORD came unto me, saying,
Eze 31:2 Son of man, speak unto Pharaoh king of Egypt, and to his multitude; Whom art thou like in thy greatness?
Eze 31:3 Behold, the Assyrian was a cedar in Lebanon with fair branches, and with a shadowing shroud, and of an high stature; and his top was among the thick boughs.
Eze 31:4 The waters made him great, the deep set him up on high with her rivers running round about his plants, and sent out her little rivers unto all the trees of the field.
Eze 31:5 Therefore his height was exalted above all the trees of the field, and his boughs were multiplied, and his branches became long because of the multitude of waters, when he shot forth.
Eze 31:6 All the fowls of heaven made their nests in his boughs, and under his branches did all the beasts of the field bring forth their young, and under his shadow dwelt all great nations.
Eze 31:7 Thus was he fair in his greatness, in the length of his branches: for his root was by great waters.
Eze 31:8 The cedars in the garden of God could not hide him: the fir trees were not like his boughs, and the chesnut trees were not like his branches; nor any tree in the garden of God was like unto him in his beauty.
Eze 31:9 I have made him fair by the multitude of his branches: so that all the trees of Eden, that were in the garden of God, envied him.
Eze 31:10 Therefore thus saith the Lord GOD; Because thou hast lifted up thyself in height, and he hath shot up his top among the thick boughs, and his heart is lifted up in his height;
Eze 31:11 I have therefore delivered him into the hand of the mighty one of the heathen; he shall surely deal with him: I have driven him out for his wickedness.
Eze 31:12 And strangers, the terrible of the nations, have cut him off, and have left him: upon the mountains and in all the valleys his branches are fallen, and his boughs are broken by all the rivers of the land; and all the people of the earth are gone down from his shadow, and have left him.
Eze 31:13 Upon his ruin shall all the fowls of the heaven remain, and all the beasts of the field shall be upon his branches:
Eze 31:14 To the end that none of all the trees by the waters exalt themselves for their height, neither shoot up their top among the thick boughs, neither their trees stand up in their height, all that drink water: for they are all delivered unto death, to the nether parts of the earth, in the midst of the children of men, with them that go down to the pit.
Eze 31:15 Thus saith the Lord GOD; In the day when he went down to the grave I caused a mourning: I covered the deep for him, and I restrained the floods thereof, and the great waters were stayed: and I caused Lebanon to mourn for him, and all the trees of the field fainted for him.
Eze 31:16 I made the nations to shake at the sound of his fall, when I cast him down to hell with them that descend into the pit: and all the trees of Eden, the choice and best of Lebanon, all that drink water, shall be comforted in the nether parts of the earth.
Eze 31:17 They also went down into hell with him unto them that be slain with the sword; and they that were his arm, that dwelt under his shadow in the midst of the heathen.
Eze 31:18 To whom art thou thus like in glory and in greatness among the trees of Eden? yet shalt thou be brought down with the trees of Eden unto the nether parts of the earth: thou shalt lie in the midst of the uncircumcised with them that be slain by the sword. This is Pharaoh and all his multitude, saith the Lord GOD.