A real problem with Premillenialism comes when you consider Christ's role as both priest and king. In Zechariah 6:12-13, a prophecy about Christ says "he shall sit and rule upon his throne; and be shall be a priest upon his throne". Hebrews 8:4 says that Christ could not act as priest while on the earth, because He did not descend from the priestly tribe of Levi(Hebrews 7:14). If Christ is unable to serve as priest on earth, yet He will serve as priest and king jointly, then His reign as king can't be an earthly reign.
I was merely point out that the author is under the misconception that the basis for premillenialism is found in Rev 20, its not, its basis is in Daniel 7.
In 2 Sam 7 the Davidic covenant is established. That references a future AND eternal kingdom. Since there can only be one eternal kingdom, the kingdom in Daniel is the awaited Davidic kingdom. The entire book of Daniel reference Earthly kingdoms, and the eternal kingdom is composed of nations, peoples, and tongues.
You cant get away from the teaching of the entire book of Daniel and an earthly kingdom by piecing together a few passages across testaments about kings and priests.
I will give you some credit though ... I have never heard this argument against premillenialism, I will have to do a little in depth work here. I appreciate the chance you have given to grow in the knowledge of scripture and wish you the same ... :-)