Is this Part 23 Final Rule document the final regulation and what are the main improvements?
The document itself is final, but it isn't the same thing as the actual regulations.

The same thing happened with the recent part 107 UAV regulations: the final rule document came first, then the regulations were published later. That means, at some point soon (?) the part 23 regulations will be updated to include the final rules you found, but I have no idea exactly when that will happen. The Part 23 final rule itself says:


  DATES: Effective [INSERT DATE 8 MONTHS AFTER DATE OF PUBLICATION IN
  THE FEDERAL REGISTER].


AOPA has a good explanation of what the rule changes will mean.