Yes, Luke 21:24, "the trodding down of Jerusalem" is from the prophesy of Daniel 7:25. It does not "allude" to it, as an "allusion" is a passing or casual reference that implies indirect similarity. The prophesy in Luke 21 is the same prophesy of Daniel 7.
But, the site you have referenced, though it has much that is correct, also is greatly confused because they have not stayed within the context of the scriptures, and so have wandered off the path in certain areas.
The focus is the trodding down of Jerusalem, not of Rome. The count of the kingdoms are the count of the succeeding world powers which began with Babylon. Dan. 7:3 defines these world powers as "four great beasts that came up from the sea". As the sea in prophesy symbolized the nations beyond the "land" or "earth" of Israel / Judah / Jerusalem, they were the pagan nations of the world beyond Jerusalem.
As first pagan nation revealed in Dan. 2:36-49, the first was Babylon described as a lion with eagles wings (Dan. 7:4). The second which devoured the first kingdom was Medo-Persian empire ruled by Cyrus and Darius and described as a bear with three ribs in its mouth - the act of devouring. The third in sequence was the Greco-Macedonian empire succeeded under Philip and his son Alexander, and described as a leopard with four heads - Alexander's four generals (Dan. 7:6).
The fourth world power that arose was the ancient world power of the Roman empire and it's description is key.
"After this I saw in the night visions, and behold a fourth beast, dreadful and terrible, and strong exceedingly; and it had great iron teeth: it devoured and brake in pieces, and stamped the residue with the feet of it: and it was diverse from all the beasts that were before it; and it had ten horns." (Dan. 7:7, KJV)
Note that the fourth world power that devoured the other three kingdoms, stamping the "residue" with its feet was different from the other three that had preceded it, and IT HAD TEN HORNS. Horns of the beasts were symbols of kings that ruled each kingdom. The ten kings were of the fourth beast. They belonged to and were out of the fourth world power, and therefore were 10 kings / rulers of Rome. They cannot have been kings or rulers of any other nation, and so were not any Zealot rulers of Jerusalem as Jerusalem was not a world power, nor a pagan nation.
The description from Dan 2:33 having feet of iron and clay is the imagery of intermixed nations as Rome had absorbed aspects of the Greco-Macedonian empire, which had absorbed elements of the Medo-Persian empire before it; which had in turn absorbed elements of the Babylonian empire before it. The different elements were not cleaving to each other, and the ancient Roman empire was not able to hold them all together.
The context of the scriptures is paramount. Dan. 7:19-25 gives us several details which define the time frame for the full establishment of Christ's heavenly kingdom.
"19 Then I would know the truth of the fourth beast, which was diverse from all the others, exceeding dreadful, whose teeth were of iron, and his nails of brass; which devoured, brake in pieces, and stamped the residue with his feet;
20 And of the ten horns that were in his head, and of the other which came up, and before whom three fell; even of that horn that had eyes, and a mouth that spake very great things, whose look was more stout than his fellows.
21 I beheld, and the same horn made war with the saints, and prevailed against them;"
The fourth world power was different from the preceeding three in several respects. The ten horns were Roman rulers. Rome began as a representative republic with senatorial provinces and regional governors that reported to the Senate, transforming over time into a Greco-Roman principate with elected consuls. But, the Roman general Gaius Julius Caesar was of the aristocracy and one of the few remaining patrician families of Rome. Through his military conquests Julius began consolidating power and with an economic and political consortium / triumvirate with Pompey and Crassus, came to be a military dictator which over-ruled the Senate in 46/45 BC, and was the ultimate cause of his assassination in 44 BC.(1)
It was under Gaius julius Caesar that Rome became the 4th world power foretold by Daniel 2 and 7. So, the first ruler or king, the first horn of that empire was Julius Caesar. The other nine kings were also of the Roman empire, and we count from Julius on to the sixth ruler which was Nero. At Nero's death, the year of four emperors occurred AD 68/69 in which three rulers who were not of the Julian line tried to take the reigns - Galba, Otho, & Vitellius.
Whereas Galba used the title of Caesar, Otho at first used the title of "Nero" before eventually adding Caesar.
"And the ten horns out of this kingdom are ten kings that shall arise: and another shall rise after them; and he shall be diverse from the first, and he shall subdue three kings." (Dan.7:24, KJV)
The confusion comes from the rendering of "after them" that makes it seem as though there were eleven kings of this kingdom. However, we have to go back to Dan.7:8 to realize that the king that subdues three others is from "among" the ten.
"I considered the horns, and, behold, there came up among them another little horn, before whom there were three of the first horns plucked up by the roots: ..." (KJV)
So, there were ten kings in all, not eleven. Beginning with Julius Caesar that makes Vespasian the tenth. The tenth was the little horn that grew in power and was different than the others before him. The difference was that Vespasian was a Flavian, not of the Julian line, and did not attempt to recall the Julian line by mimicking Nero as both Galba, and Otho had done.
The tenth king / ruler put down three before him. Galba, Otho and Vitellius all attempted to grasp the reigns of Rome during the "time, times, and half a time" (Dan. 7:25) when Vespasian was sent to put down the rebellion in Judea. It was during that second year of the Roman-Jewish wars that Vespasian had to break off and lead his troops back to Rome to take control of the empire. He left his son Titus in charge of the war in Judea.
Titus did not put down or abase his father. Titus inherited the throne from his father Vespasian. So, Titus cannot have been the little horn that put down three others before him. That was Vespasian.
The "end" of the prophesies of Daniel was not the end of the Roman empire, nor the end of the line of the Caesars. The end would occur during that fourth kingdom, and was the end of the desolations of Jerusalem (Dan. 12:6-7). The destruction of the temple in Jerusalem was the focus. It was the end of the Mosaic covenant; the end of the animal sacrificial system in that temple. And, that was time when all power was given to Christ as the fullness of the heavenly kingdom was brought into all power over all of the kingdoms of the earth.
The end of the prophesies was the destruction of the temple in Jerusalem in AD 70, and that was the fulfillment of the trodding down of Jerusalem by the gentiles. (2) (3)
"But the court which is without the temple leave out, and measure it not; for it is given unto the Gentiles: and the holy city shall they tread under foot forty and two months." (Rev. 11:2, KJV)
1) Julius Caesar - here
2) Frequent Mistakes - Part I: Rev. 13:3 The Wounded Head here
3) Frequent Mistakes - Part II: The Ascension of Christ here