"The devil, who deceived them, was cast into the lake of fire and brimstone where the beast and the false prophet are [or were cast, as many acknowledge this should be rendered]. And they will be tormented day and night forever and ever" (Revelation 20:10 Revelation 20:10And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
American King James Version×).

Does this verse say that these two end-time individuals, the Beast and False Prophet, will be tormented for eternity?

The Beast and False Prophet are human beings. While still alive, they will be cast into the lake of fire. "Then the beast was captured, and with him the false prophet who worked signs in his presence, by which he deceived those who received the mark of the beast and those who worshipped his image. These two were cast alive into the lake of fire burning with brimstone" (Revelation 19:20 Revelation 19:20And the beast was taken, and with him the false prophet that worked miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.
American King James Version×).

We see from Malachi 4:1-3 Malachi 4:1-3 [1] For, behold, the day comes, that shall burn as an oven; and all the proud, yes, and all that do wickedly, shall be stubble: and the day that comes shall burn them up, said the LORD of hosts, that it shall leave them neither root nor branch. [2] But to you that fear my name shall the Sun of righteousness arise with healing in his wings; and you shall go forth, and grow up as calves of the stall. [3] And you shall tread down the wicked; for they shall be ashes under the soles of your feet in the day that I shall do this, said the LORD of hosts.
American King James Version×and Mark 9:47-48 Mark 9:47-48 [47] And if your eye offend you, pluck it out: it is better for you to enter into the kingdom of God with one eye, than having two eyes to be cast into hell fire: [48] Where their worm dies not, and the fire is not quenched.
American King James Version×that any human being thrown into the lake of fire will be destroyed. He will perish. His punishment will be eternal. But he will not be tormented for eternity.

Revelation 20:10 Revelation 20:10And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever.
American King James Version×is speaking of Satan the devil being cast into the lake of fire at the end of Christ's 1,000-year reign. Reference to the Beast and False Prophet being cast in is only parenthetical here—as they will have died when that happened 1,000 years earlier. They will not still be burning there. Thus being tormented "forever and ever" applies principally to Satan—and presumably to his demonic cohorts as well (compare Matthew 25:41 Matthew 25:41Then shall he say also to them on the left hand, Depart from me, you cursed, into everlasting fire, prepared for the devil and his angels:
American King James Version×).

Furthermore, it should be pointed out that the Greek phrase translated "forever and ever" here, eis tous aionas ton aionon, literally means "unto the ages of the ages." While this might mean for eternity, it could also mean until the culmination of the ages, which would allow for an ending point soon after the casting into the fire.