Please learn how to post code and monospaced error text to the forum:
The first output you showed, indicates that the gem was correctly installed.
After that callng
require 'zip'
… should have unshifted the path to the RubyZip gem’s “lib” subfolder into the first position of the $LOAD_PATH array, and then loaded …
"%AppData%/SketchUp/SketchUp 2021/SketchUp/Gems64/gems/rubyzip-2.3.0/lib/zip.rb"
… which loads most of the files in the lib’s "zip" subfolder.
Following this, the Zip module should be defined at the top level ObjectSpace.
I just tried it in SU2021 and it worked fine for me.
Suggest you restart SketchUp and retry.