No, Rome fell but the Church remained. It didn't conquer Rome -- in Christ, we are far more than conquerers (Romans 8). As an aside on the "martial spirit of imperial Rome", one of the reasons Rome fell was because imperial Rome lost the martial spirit of the Republic. The spirit of Virtus was lost, the Equestrian class ceded their role to the NCO class of the legions and so forth, I won't trouble you with the technical details but you get the drift.
"The church had changed its nature, had become a political organization in the spirit and pattern of imperial Rome."
The Bible outlines that Churches should have organization. When you have a worldwide Church, you have worldwide organization. Nothing sinister here.
"The imperial church of the 4th and 5th centuries had became an entirely different institution from the church of the first three centuries. In its ambition to rule it lost the Spirit of Christ."
Says you, or whoever wrote this tripe.
"Worship, at first very simple, was developed into elaborate, stately, imposing ceremonies having all the outward splendor that belonged to Rome."
No splendor belongs to Rome, or the Pope, or America. All splendor belongs to God alone.
"The church became an amalgamation of pagan philosophies. The church lost sight of its true mission."
No it didn't and no it didn't -- the author says yop yop yop, the only response required is nop nop nop.
From inside your Roman fish bowl, it’s tripe. For us outside the fish bowl, it’s quite obvious. I take my leave now. Have a good day.